SATHEE: Permutations And Combinations Question 356

Permutations And Combinations Question 356

Question: A seven digit number divisible by 9 is to be formed by using 7 out of number $ {1,2,3,4,5,6,7,8,9} $ . The number of ways in which this can be done is

Options:

A) $ 7! $

B) $ 2\times 7! $

C) $ 3\times 7! $

D) $ 4\times 7! $

Show Answer

Answer:

Correct Answer: D

Solution:

[d] Sum of 7 digits = a multiple of 9 Since sum of number 1, 2, 3? 8, 9 is 45 (Since a number is divisible by 9 if sum of its digits is divisible by 9.) So, two left number should also have sum as 9. The pairs to be left are (1, 8) (2, 7) (3, 6) (4, 5) with each pair left, number of 7 digit numbers $ =7! $ . So, with all 4 pair?s total seven digits number $ =4\times 7! $

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Permutations And Combinations Question 356

Question: A seven digit number divisible by 9 is to be formed by using 7 out of number $ {1,2,3,4,5,6,7,8,9} $ . The number of ways in which this can be done is

Options:

Answer:

Solution:

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