Permutations And Combinations Question 350
Question: 5 - Digit numbers are to be formed using 2, 3, 5, 7, 9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000, then p:q is:
Options:
A) $ 6:5 $
B) $ 3:2 $
C) $ 4:3 $
D) $ 5:3 $
Correct Answer: D $ \therefore $ All numbers 2, 3,5,7,9 can come at first place. $ q:\underset{5}{\mathop{TTH}}\underset{4}{\mathop{TH}}\underset{3}{\mathop{H}}\underset{2}{\mathop{T}}\underset{1}{\mathop{0}}\begin{matrix} place \\ ways \\ \end{matrix} $ Total no. of ways $ =4\times 4!=96 $ ( $ \because $ 2 and 9 cannot be put at first place) So, $ p:q=120:96=5:4 $
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BETA
