Permutations And Combinations Question 321
Question: The total number of 5 digit numbers of different digits in which the digit in the middle is the largest, is
Options:
A) $ \sum\limits _{n=4}^{9}{^{n}P_4} $
B) $ \sum\limits _{n=4}^{9}{^{n}P_4}-\frac{1}{3!}\sum\limits _{n=3}^{9}{^{n}P_3} $
C) $ 30(3!) $
D) None of these
Correct Answer: DShow Answer
Answer:
Solution:
$ \therefore $ The required number of numbers $ ={{(}^{4}}P_4{{-}^{3}}P_3)+{{(}^{5}}P_4{{-}^{4}}P_3)+{{(}^{6}}P_4{{-}^{5}}P_3)+…+{{(}^{9}}P_4{{-}^{8}}P_3) $ $ =\sum\limits _{n=4}^{9}{^{n}P_4-\sum\limits _{n=3}^{8}{^{n}P_3}} $
BETA
