Question

A team of 5 watchers is to be chosen from 4 sophomores, 3 juniors, and 2 seniors. How many teams can be formed if the team is to include 2 sophomores, 2 juniors, and 1 senior? ​

Answer 1

Answer:

1 team can be formed and remain 2 sophomore, 1 junior, 1 senior

Answer 2

Answer:

Concept - Permutations and combinations

Given - A team of 5 watchers is to be chosen from 4 sophomores, 3 juniors, and 2 seniors.

To find - No. of teams which can be formed if the team is to include 2 sophomores, 2 juniors, and 1 senior

Step-by-step explanation:

As we know that total number if watcher which can be choose is 5

As we know the permutation formula = $nc_{r} = \frac{n!}{(n-r)!*r!}$

We can use this formula to find the number of teams which can be formed.

So, by selecting only 2 sophomores from 4  we get,

$4c_{2} =\frac{4!}{(4-2)!*2!} =\frac{4*3}{2*!} =6ways$

Now for selecting only 2 juniors from 3 we get,

$3c_{2} = \frac{3*2}{1*2} = 3 ways$

For selecting 1 senior from 2 we get,

$2c_{1} =\frac{2!}{(2-1)!*1!} = 2 ways$

So, total number of team which can be form = $6+3+2 = 11$

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