Test Index

NCERT Class XI Mathematics - Permutations and Combinations - Solutions

© examsnet.com
Question : 22 of 41
Marks: +1, -0
If  nC8\,{}^nC_8 =  nC2\,{}^nC_2 , find  nC2\,{}^nC_2
Solution:  
We have ,  nC8\,{}^nC_8 =  nC2\,{}^nC_2
⇒  nC8\,{}^nC_8 =  nCn−2\,{}^nC_{n-2} [Since  nCr\,{}^nC_r =  nCn−r\,{}^nC_{n-r}]
⇒ 8 = n - 2 [Since  nCa\,{}^nC_a =  nCb\,{}^nC_b ⇒ a = b] ⇒ n = 10
∴  nC2\,{}^nC_2 =  10C2\,{}^{10}C_2 = 10!2!8!\frac{10!}{2!8!} = 10×92\frac{10 \times 9}{2} = 45
© examsnet.com
Go to Question:
Prev Question
Next Question