Permutations And Combinations Question 112
Question: The least value of natural number n satisfying $ C(n,5)+C(n,6)>C(n+1,5) $ is [EAMCET 2002]
Options:
A) 11
B) 10
C) 12
D) 13
Correct Answer: A
Show Answer
Answer:
Solution:
Þ $ ^{n+1}C_6>{{}^{n+1}}C_5 $
Þ $ \frac{(n+1)!}{6!.(n-5)!}.\frac{5!.(n-4)!}{(n+1)!}>1 $
Þ $ \frac{(n-4)}{6}>1 $
Þ $ n-4>6\Rightarrow n>10 $ Hence according to options n = 11.
BETA
