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# in how many ways 10 boys and 9 girls can be seated in a row so that they are alternate?

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## In how many ways can 10 boys and 10 girls sit in a row so that no two boys sit together ?

10 boys and 10 girls sit in a row so that no two boys sit together. So a boy is to be seated between two girls or at the two ends of the row. So the boys are to be seated in 11 positions in ""^11C10 ways. Again 10 boys and 10 girls can be arranged among themselves in 10! and 10! ways respectively. :."The total number of ways = ""^11C10xx10! xx10! =(11)! xx (10)!

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In how many ways can 10 boys a...

In how many ways can 10 boys and 10 girls sit in a row so that no two boys sit together ?

Updated On: 27-06-2022

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10 boys and 10 girls sit in a row so that no two boys sit together. So a boy is to be seated between two girls or at the two ends of the row. So the boys are to be seated in 11 positions in

11 C 10 11C10

ways. Again 10 boys and 10 girls can be arranged among themselves in 10! and 10! ways respectively.

∴The total number of ways =

11 C 10

×10!×10!=(11)!×(10)!

∴The total number of ways = 11C10×10!×10!=(11)!×(10)!

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स्रोत : brainly.in

## In how many ways can five boys and four girls be seated in a row of nine chairs when the boys and girls must sit in alternate chairs?

Answer: There are total 9 chairs in the row. On them, 5 boys and 4 girls are to be so arranged that boys and girls must sit on alternate chairs. So, when 9 chairs are placed in a row; the boys must occupy the first, third, fifth, seventh and ninth chairs, leaving the second, fourth, sixth and ei...

In how many ways can five boys and four girls be seated in a row of nine chairs when the boys and girls must sit in alternate chairs?

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Sort Jayanta Mukherjee

B Tech IEE in Instrumentation Engineering, Jadavpur University (Graduated 1990)Author has 13.4K answers and 5.9M answer views1y

There are total 9 chairs in the row. On them, 5 boys and 4 girls are to be so arranged that boys and girls must sit on alternate chairs.

So, when 9 chairs are placed in a row; the boys must occupy the first, third, fifth, seventh and ninth chairs, leaving the second, fourth, sixth and eighth chairs for the girls.

Thus, five boys can be arranged in (5!) = 120 ways; and, for every arrangement of the boys, the four girls can be arranged in (4!) = 24 ways.

So, the answer will be (120 * 24) = 2880.

518 views Eric Widdison

Electrical Engineer (2004–present)Author has 2.5K answers and 1.1M answer views1y

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5 girls and 5 boys are required to sit in a row of 10 chairs so that no one is seated next to anyone of the same gender. How many ways can this be done with a boy sitting between two girls?

Originally Answered: 5 girls and 5 boys are required to sit in a row of 10 chairs so that no one is seated next to anyone of the same gender. How many ways can this be done until a boy sits between two girls?

What you describe is a seating arrangement that can go either bgbgbgbgbg or gbgbgbgbgb. Since the seats are in a row, the seats are distinct, as are the boys and girls, so you can arrange the 5 boys in 5! ways and the 5 girls in 5! ways, and there are 2 ways to choose who goes first, giving a total of 2(5!)(5!)=28,800 different arrangements.

If they had been sitting in a circle and the chairs were not distinct then you can pick any one person (say the youngest girl) and have their chair count as the first chair. That would reduce the number of arrangements by a factor of 10 (because in only 1/1

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In how many ways can 5 boys and 4 girls be arranged on a bench if boys and girls are in separate groups? If Anne and Jim wish to stay together?

You can think of the problem as how many different permutations of a line is possible under the restrictions that are mention in the question, because the only significant factor are the different orders that the kids can be placed in. To further visually cement this idea, one can imagine an indexed set of positions (or an array for us computer science majors).

So since the boys and the girls are separated in groups then either all of the boys sit on the right and the girls sit on the left or visa verca. let’s consider the instance where the girls sit on the left.

Since the love birds JIm and An

Ved Prakash Bhawsar

Freelancer - Internet Business Guy4y

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In how many ways can 4 boys and 5 girls be seated alternately?

There can be only one arrangement in which boys and girls can sit.

G-B-G-B-G-B-G-B-G

but position of individual boy and girls can be changed.

So, there are 5 girls and 5 slots for them that means they can be arranged in 5! ways,

similarly boys have 4 slots, so they can be arranged in 4! ways.

now, one more thing to consider is that out of 5! arrangements of girls, with each arrangement boys can be arranged in 4! different positions.

so to get the total number of boys and girls arrangements together we would need to multiply the arrangements of both boys and girls.

so the desired answer would be: 5!*4

Amisha Bhaskar

B.E from Netaji Subhas Institute of Technology (Graduated 2022)3y

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4 girls and 5 boys are to be seated in a row on 9 chairs in such a way that all the four girls always sit together. In how many different ways can it be done?

4 girls are sitting together. So, consider them to be single entity. When arranged with 5 boys the arrangement will be in 6!

Now those four girls will arrange themselves 4! Ways .

So, total arrangement we get is 6!*4!

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Prakash Raj

Its all about arrangement and selectionAuthor has 200 answers and 1M answer views4y

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In how many ways can 5 boys and 3 girls sit on 8 chairs if all girls sit together?

keep all the girls together and consider them as one entity

so there will be 5 boys and one entity (consisting of three girls) = 6 persons

6 persons can be arranged in 6! ways

also 3 girls tied together can be arranged in 3! ways

so answer is 6!*3! Terry Richards

Programming for Over 40 Years (1975–present)Author has 199 answers and 94.4K answer viewsMay 20

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Mohammed 7 day ago

Guys, does anyone know the answer?