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atroni [7]
3 years ago
6

How many 5-member chess teams can be chosen from 15 interested players? Consider only the members selected, not their board posi

tions. 3,003 120 360,360
Mathematics
1 answer:
ryzh [129]3 years ago
7 0

<u>Answer</u>:

3003 number of 5-member chess teams can be chosen from 15 interested players.

<u>Step-by-step explanation:</u>

Given:

Number of the interested players =  15

To Find:

Number of 5-member chess teams that can be chosen = ?

Solution:

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formulanCr = \frac{n!}{r!(n - r)!}

where

n represents the total number of items,

r represents the number of items being chosen at a time.

Now  we have n = 15 and r = 5

Substituting the values,

15C_5 = \frac{15!}{5!(15- 5)!}

15C_5 = \frac{15!}{5!(10)!}

15C_5 = \frac{15!}{5!(10)!}

15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{5 \times 4 \times 3 \times 2 \times 1(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)}

15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11}{(5 \times 4 \times 3 \times 2 \times 1)}

15C_5 = \frac{360360}{120}

15C_5 = 3003

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