Question

Please calculate in how many ways can a set of 5 players be formed out of the total of 10 players such that two particular players should be involved in each set?

Answer 1

Given that:

A set of 5 players be formed out of the total of 10 players such that two particular players should be involved in each set.

To find: No.of ways of selection

Solution: This is a question of selection,so using combination one can easily calculate total number of ways of selection according to given criterion.

No. of ways of selection of r players from n players

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

Here in the given question:

n=10

r=5

* But out of these five 2 particular players are already selected,so

Now,Total players from selection to be made n = 10-2= 8

Total players to be select r= 5-2= 3

$^{8}C_3 = \frac{ 8! \: }{3! \times(8-3)! } \\ \\ = \frac{ 8! \: }{5! \times3! } \\\\ = \frac{8 \times 7 \times 6 \times 5!}{5! \times 3 \times 2} \\ \\ = 8 \times 7 \\ \\ Total\:ways= 56$

Total 56 ways are there .

Hope it helps you.

Answer 2

Answer:

A set of 5 players be formed out of the total of 10 players such that two particular players should be involved in each set.

Solution: This is a question of selection ,so using combination one can easily calculate total number of ways of selection according to given criterion. Total 56 ways are there