(C) The number of ways to select $r$ items from a set of $n$ items is given by the combination formula: $C(n, r) = \frac{n!}{r!(n-r)!}$.Here,$n = 10$

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(C) The number of ways to select $r$ items from a set of $n$ items is given by the combination formula: $C(n, r) = \frac{n!}{r!(n-r)!}$.Here,$n = 10$ and $r = 5$.Therefore,the number of ways $= C(10, 5) = \frac{10!}{5!5!}$.$= \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}$.$= \frac{30240}{120} = 252$.

Competitive Quantitative Aptitude Permutation and Combination Permutation and Combination

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In how many ways can $5$ sportsmen be selected from a group of $10$?

A
$272$
B
$282$
C
$252$
D
$242$

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In how many ways can $5$ sportsmen be selected from a group of $10$?

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The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$ is

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