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The number of integers greater than 6...

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is : (1) 216 (2) 192 (3) 120 (4) 72

A

216

B

192

C

120

D

72

Text Solution

Verified by Experts

The correct Answer is:
B
The integer greater than 600 may be of 4 digits or 5 digits. So, here two cases arise.
Case I When number is of 4 digits.
Four - digit number can start from 6, 7 or 8.
Thus, total number of 4 - digit numbers, which are greater than `6000 = 3 xx 4 xx 3 xx 2 = 72`
Case II When number is of 5 digits.
Total number of five-digit numbers which are greater than `6000 = 5! = 120`
`therefore` Total number of integers = 72 + 120 = 192
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