Question

A pool a possible candidate for a student council consists of 14 freshmen and 8 softwares how many different councils consisting of 5 freshmen and 7 sophomores are possible

Answer 1

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

We have given that,

A pool of possible candidates for a student council consists of 14 freshmen and 8 software.

We have to determine the how many different councils consisting of 5 freshmen and 7 sophomores are possible

What is the combination?

$_n C_r=\frac{n !}{r ! (n-r) !}_n C_r = number of combinations\\\n = total number of objects in the set\\\r = number of choosing objects from the set$

The total number of the council is

$_{10} C_5\times _9 C_7$

=252(36)

=9216

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

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