How many numbers can be formed from digits 1, 3, 5, 9 if repetition of digits is not allowed?

Answer

64

Explanation

One-digit numbers:
Clearly, there are four 1 -digit numbers.
Two-digit numbers:
We may fill the unit's place by any of the four given digits.
Thus, there are 4 ways to fill the unit's place.
The ten's place may now be filled by any of the remaining three digits. So, there are 3 ways to fill the ten's place.
Number of 2-digit numbers `=(4xx3)=12.`
Three-digit numbers:
Number of ways to fill the unit's, ten's and hundred's places are 4, 3 and 2 respectively.
Number of 3-digit numbers `=(4xx3xx2)=24.`
Four-digit numbers:
Number of ways to fill the unit's ten's, hundred's and thousand's places are 4, 3, 2 and 1 respectively.
Number of 4-digit numbers `=(4xx3xx2xx1)=24.`
Hence, the number of required numbers `=(4+12+24+24)=64.`