Question

How many 4-digits number can be formed out of 0,1,2,3,5,7 and 8. If:

the number must be even with no repetition, then with repetition

Answer 1

Below in bold.

Explanation:

No repetition.

There are a total of 7 numbers.

For the number to be even it must end in 0, 2 or 8.

The other 3 numbers will be the number of permutations of 3 from the 6 other numbers.

Number of 4 digit numbers ending in 0

= 6P3 = 6! / 6-3!

= 120.

Now the number could also end in 2 or 8,

so there are 3*120 = 360 4-digit even numbers (no repetition).

With repetition.

There are 3 * 7^3 = 1029 with repetition.