How many poker hands contain a full house without any diamon

How many poker hands contain a full house without any diamonds? (For instance, Jsp Jcl Jhe 7he 7cl is one such hand.)

Solution

If no diamonds needs to be selected

Then we need to select one pair and one triplet

Selecting one pair = 13 * 12 = 156 ways

Selecting one triplet = 3C3 = 1 way (since we want to select all numbers of one kind and there are only three suits left after removing the diamonds, hence number of ways will be)

Number of Choices = 78 * 1 * 3C2(2 pairs can be selected from any of the possible three suits) = 156 * 3 = 468 ways