Question

When n=8 and r=3, find the
number of selections. *
O
47
ООО
48
45​

Answer 1

Given : n=8 and r=3

To Find : the  number of selections.

47

56

48

45​

Solution:

number of selections of selecting r items from n items

$= {^n}C_r$

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

n = 8

r = 3

Hence

${^8}C_3 = \dfrac{8!}{3!(8-3)!}$

 $\implies {^8}C_3 = \dfrac{8!}{3!5!}$

 $\implies {^8}C_3 = \dfrac{8.7.6.5!}{3!5!}$

 $\implies {^8}C_3 = \dfrac{8.7.6}{3!}$

$\implies {^8}C_3 = \dfrac{8.7.6}{6}$

$\implies {^8}C_3 = 8.7$

$\implies {^8}C_3 = 56$

⁸C₃ = 56

number of selection  = 56

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