Question

The number of ten digit numbers that contain only 2 and 3 as its digit, but no any pairwise 3's
joins together, is
​

Answer 1

Solution:

When exactly one 3′s are used, then numbers possible = 10 C 1

When exactly two 3′s are used, then numbers possible = 9 C 2

When exactly two 3′s are used, then numbers possible = 8 C 3

When exactly two 3′s are used, then numbers possible = 7 C 4

When exactly two 3′s are used, then numbers possible = 6 C 5

well use only 5 3's coz if we use more then the case is not possible

Adding all =143