Question

There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter? 720 810 5,005 3,603,600

Answer 1

The no. of different groups of players of 6 players , if the position does not matter is given by 5005 ,Option C is the right answer.

What is Combination ?

Combination is a method of selection of items from a set of distinct objects , when the position doesn't matter .

It is given that

Total number of players = 15 = n

No. of players to be selected = 6 = r

The no. of different groups of players of 6 players , if the position does not matter is given by

$\rm ^nC_r = \dfrac{n!}{r! (n-r)!}$

So

$\rm ^{15}C_6 = \dfrac{15!}{6! (15-6)!}\\\\\rm ^{15}C_6 = \dfrac{15!}{6! (9)!}\\\\\\^{15}C_6 = \dfrac{15 * 14 * 13* 12 * 11 * 10 }{6 *5* 4 * 3 * 2*1}\\\\ ^{15}C_6 = 5005$

Therefore , The no. of different groups of players of 6 players , if the position does not matter is given by 5005

Option C is the right answer.

To know more about Combination

https://brainly.com/question/19692242

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