Five digit numbers are formed from digits 4, 5, 6, 7 and 8.
(a)How many such numbers can be formed if repitition of digits is (i) allowed (ii) not allowed?
(b) How many of the numbers are odd, if repetition of digits is not allowed?
(a)(i) If repetition is allowed, the numbers can be formed as follows:
| Position | 1st | 2nd | 3rd | 4th | 5th |
| Ways | 5 | 5 | 5 | 5 | 5 |
Number of ways = \(5^{5} = 3125\)
(ii) If no repetition = \(5!\) ways
= 120 ways
(b) No repetition and the numbers odd
The 5th position is filled by 5 and 7 for it to be odd ie 2 ways
| Position | 1st | 2nd | 3rd | 4th | 5th |
| Ways | 4 | 3 | 2 | 1 | 2 |
Ways = \(4 \times 3 \times 2 \times 1 \times 2 = 48\)
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