QA – Placement Quizzes | Permutation and Combination | Question 6

How many 4-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 which are divisible by 5 when none of the digits are repeated?
(A) 120
(B) 35
(C) 24
(D) 720


Answer: (A)

Explanation: A number is divisible by 5 if and only if its last digit is either 5 or 0. But, 0 is not available here. So, we have to fix 5 as a last digit of 4-digit number and fill 3 places with remaining 6 digits.
Number of ways to choose 3 digits = 6C3 = 20.
Number of ways to arrange the chosen digits = 3!
Hence, total number of required ways = 6C3 * 3! = 6P3 = 120.

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