Mathematics: What is the value of the expression 10 c 6? a.210 b.720 c.5040 d.151,200

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What is the value of the expression 10 c 6? a.210 - id1062104903063, Sushmitarai9416

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EMscary4996

17.01.2022

Mathematics

A. 210

Step-by-step explanation:

We know that the number of combinations of n things taking r at time is given by expression :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$ (1)

The given expression : $^{10}C_{6}$ which basically gives the number of combinations of 10 things taking 6 at a time.

Using (1) , we have

$^{10}C_{6}=\dfrac{10!}{6!(10-6)!}\\\\=\dfrac{10\times9\times8\times7\times6!}{6!4!}\\\\=\dfrac{10\times9\times8\times7}{4!}\ \ [\text{Cancel }6!\text{ from numerator and denominator}]\\\\=\dfrac{10\times9\times8\times7}{4\times3\times2\times1}\\\\=210$

Hence, the correct answer is A. 210 .

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What is the value of the expression 10 c 6? a.210 b.720 c.5040 d.151,200

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