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If none of the digits 3, 5, 7, 8, 9 be r...

If none of the digits `3, 5, 7, 8, 9` be repeated, how many different numbers greater than 7000 can be formed with them?

A

190

B

192

C

180

D

185

Text Solution

Verified by Experts

The correct Answer is:
B
Here, we have to find the number of integers greater than 7000 with the digits 3, 5, 7, 8 and 9. So, with these digits we can make maximum five-digit number because repeatition is not allowed.
Now, all the five-digit numbers are greater than 7000.
Number of ways of forming 5-digit number `= 5 xx 4 xx 3 xx 2 xx 1 = 120`
and all the four - digit numbers greater than 7000 can be formed in following manner.
Thousand place can be filled in 3 ways. Hundred place can be filled in 4 ways. Tenth place can be filled in 3 ways. units place can be filled in 2 ways.
Thus, we have total number of 4-digit number `= 3 xx 4 xx 3 xx 2 = 72`
`therefore` Total number of integers = 120 + 72 = 192
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