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?

Question

siddharth · Answer

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?

anonymous · Answer

oo. sory :) yep

shaik0124 · Answer

25c8+17c7=     add this u will get the answer

anonymous · Answer

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

siddharth · Answer

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

zarkon · Answer

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

siddharth · Answer

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?

anonymous · Answer

correct

shaik0124 · Answer

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

anonymous · Answer

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