Question

2.In how many ways can a committee of 5 be formed from 7 juniors and 6 seniors if the
committee must have 3 juniors?​

Answer 1

Given :  a committee of 5 be formed from 7 juniors and 6 seniors if the

committee must have 3 juniors

To Find : Number of ways

Solution:

Junior = 7

Senior = 6

committee must have 3 juniors

committee of 5

3 junior  + 4 junior + 5 junior

= ⁷C₃*⁶C₂  + ⁷C₄*⁶C₁  + ⁷C₅*⁶C₀

= 35 * 15 + 35 * 6  + 21*1

= 35 * 21  + 21

= 36 * 21

=  756

756 ways  committee can be formed

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Answer 2

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According to the Question

We need to select a committee of 5 from 5 juniors and 7 seniors.

Now 3 of seniors are to be selected.

So, that we need 2 members from total of 5 juniors and 4 seniors.

Case 1

Where both are juniors

So, we need 5 C 2 i.e. 10 cases

Case 2

Where 1 is junior and other is senior

So we need 5 C 1 +4 C 1 i.e. 9

Case 3

Where both are seniors

Here we need 4 C 2 i.e. 6

So total cases

=10+9+6

$\boxed{ = > 25}$

So, 25 are the total cases

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