## siddharth 3 years ago Combinatorics question: There are 42 kids in a class, 25 girls and 17 boys. I need to choose 15 kids to form a team. In how many ways can I get at least 7 boys?

1. siddharth

Thanks for your reply but I dont understand how you get that 18 girls number. I need a team of total 15 kids out of which at least 7 need to be boys, so at max we can have 8 girls... did you mean 8?

2. bob06

oo. sory :) yep

3. shaik0124

4. bob06

you need have 7 boys and 8 girls so, if you have 25 girls and you only need 8, you will have 17 left over you will also have 10 boys left over these kids can be swapped out for other kids http://www.mathsisfun.com/combinatorics/combinations-permutations.html

5. siddharth

how did you get that shaik? can you explain please?

6. Zarkon

$\sum_{x=7}^{15}{25\choose 15-x}{17\choose x}$

7. siddharth

The way I understand it, i need to have at least 7 boys. The rest 8 places can be either girls or boys... is that correct?

8. bob06

correct

9. shaik0124

select 7 from 17 and this can b done in 17c7 ways + select 8 from 25 in 25c8 ways bcz u require atleast 7 then u have to select 7 boys compulsory to form a team+ remaing from boys r girls

10. bob06

look at the website I gave a link for for an easy to understand review :)