Permutations And Combinations Question 205
Question: If $ P(n,r)=1680 $ and $ C(n,r)=70 $ , then $ 69n+r!= $ [Kerala (Engg.)2005]
Options:
A) 128
B) 576
C) 256
D) 625
Show Answer
Answer:
Correct Answer: B
Solution:
- $ P(n,r)=1680 $ $ \frac{n!}{(n-r)!}=1680 $ ?..(i) $ C(n,r)=70 $
Þ $ \frac{n!}{r!(n-r)!}=70 $ ?..(ii) $ \frac{1680}{r!}=70 $ , [From (i) and (ii)] $ r!=\frac{1680}{70}=24 $
Þ $ r=4 $ $ \because P(n,4)=1680 $ $ \because $ $ n(n-1)(n-2)(n-3)=1680 $
Þ $ n=8 $ $ \because $ $ 8\times 7\times 6\times 5=1680 $ Now $ 69n+r!=69\times 8+4! $ $ =552+24 $ = 576.
BETA
