Permutations...

Asked by sashank2 | 28th Feb, 2010, 03:00: PM

Expert Answer:

(c) 101.

At least 2 digits should be identical, which means we'll not have any 4 digit numbers with distinct digits.

Divisible by 5 requires the units digit of the 4 digit number to be fixed at 5.

Now we have to select THREE more digits, to select each out of the three we have 5 different choices, 1,2,3,4 and 5, as the digits can be repeated.

Hence the total number of ways = 5x5x5 = 125.

Now the 4 digit numbers with distinct digits, no repeatations, so the selection of three digits, we have only 1,2,3 and 4 available.

First digits can be selected in 4 ways,

Second in 3 ways,

Third in 2 ways.

Total number of distinct digits, 4x3x2 = 24.

So the required 4 digit numbers, 125-24 = 101.

Regards,

Team,

TopperLearning.

Answered by  | 28th Feb, 2010, 07:20: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.