Question

A school captain and 2 vice-captains are to be chosen from a group of 5 boys and 6 girls. What is the probability that all 3 positions will be taken by:
at least two girls?

Answer 1

Here we will use the concept that I was applying that day I guess..

Answer 2

Firstly find the total number of combinations you can choose to form Captain and Vice captains..

You can do that in :

\[\large ^{11}C_3\]

Answer 3

And note that the word "Atleast " comes here..

Answer 4

3 positions taken by at least 2 girls has the following 2 cases:
1) 2G and 1B
2) 3G and 0B

no. of ways for (1) is 6C2 * 5C1
no. of ways for (2) is 6C3 * 5C0

so the total no. of ways for at least 2 girls is (6C2 * 5C1) + (6C3 * 5C0)
for the probability, divide that exp by the total no. of ways for selecting the captains = 11C3

Answer 5

Atleast means you can have 2 girls out of 3 or you can have 3 out of 3 also..

SO:
\[^6C_2 \times ^5C_1 + ^6C_3\]

Answer 6

huh?

Answer 7

sorry, explain please :(

Answer 8

which part is confusing u?

Answer 9

I am making the combinations so check this:


2 girls And 1 boy Or 3 girls AND 0 boy..

\(^6C_2\) \(\times \) \(^5C_1\) + \(^6C_3\) \(\times\) \(^5C_0\)



2 girls out of 6 you can choose in \(^6C_2\)
1 boy you can select in out of 5 : \(^5C_1\)

3 girls out of 6 you can have in : \(^6C_3\)

0 boys out of 5 you can have in : \(^5C_0\)

Answer 10

ok got it, thanks.

Answer 11

Sure no ??

Answer 12

ya, sure.

Answer 13

Solve it and try to find out the answer..

Answer 14

yep, got it.

Answer 15

Well Done..