Given,
Digits which can be used to make numbers are 1, 2, 3, 4 and 5
The number of these digits are 5
To find : Total number of 4-digit numbers with no digit repeated
Formula used :
Number of arrangements of n things taken r at a time = P(n, r)
P(n, r) = \(\frac{n!}{(n-r)!}\)
∴ The total number of ways
= the number of arrangements of 5 things taken 4 at a time
= P(5, 4)
= 120
Hence,
Total number of 4-digit numbers using digits 1 to 5 with no digit repeated are 120
Now,
For 4-digit even number from digits 1, 2, 3, 4 and 5 :
Let 4-digit even number be
Fix the position of unit’s place i.e. t as an even number for which we have 2 choices (2 or 4)
Now,
For position x we have remaining 4 choices.
Similarly,
For position y and z we have 3 and 2 choices respectively
Total number of even numbers are :
= multiplication of choices of x y z t
= 4 × 3 × 2 × 2
= 48
Hence,
Total number of 4-digit numbers using digits 1 to 5 with no digit repeated are 48.