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Question
Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are divisible by 5
Solution
There are 6 different digits and we have to form 6-digit numbers, i.e., n = 6, r = 6
If no digit is repeated, the total numbers with 6-digits can be formed = nPr
= 6P6
= 6!
= 6 x 5 x 4 x 3 x 2 x 1
= 720.
Since the number is divisible by 5, the unit's place of 6-digits number can be filled in only one way by the digit 5.
Remaining 5 positions can be filled from the remaining 5 digits in 5P5 ways.
Hence, the total number of 6-digit numbers divisible by 5 = 1 x 5P5 = 5!
= 5 x 4 x 3 x 2 x 1
= 120.
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