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Question

Mathematics Question on permutations and combinations

If 10Cx=10Cx+4{^{10}C_{x}} = {^{10}C_{x + 4}}, find the value of x.

A

5

B

4

C

3

D

2

Answer

3

Explanation

Solution

We have 10Cx=10Cx+4{^{10}C_{x}} = {^{10}C_{x+4}} ⇒ x+x+4=10 ⇒ 2x=6 ⇒ x=3\Rightarrow \, x + x + 4 = 10 \, \Rightarrow \, 2x = 6 \, \Rightarrow \, x = 3