Question

25. A couple is expecting the birth of a baby boy. They will name the boy by choosing a first name and a middle name from this list of their favorite boys' names: Billy, Bobby, Buster, Bubba. They have not ruled out the possibility that the child's first and middle names will be the same (example: Billy Buster, Buster Billy, and Bubba Bubba are three different, valid possibilities).

a) How many different names are possible?

b) The first and middle names will be different?

Answer 1

There are 4 names to choose from:

a)

Number of ways to pick up first name = 4C1 = 4

Number of ways to pick up Middle name = 4C1 = 4

Total Number of ways = 4C1 * 4C1 = 4*4 = 16

b) Number of ways when first and middle names will be different

Number of ways to pick up first name = 4C1 = 4

Number of ways to pick up Middle name [Now since first names will different, we have only 3 option to pick from] = 3C1 = 3

Total Number of ways = 4C1 * 3C1 = 4*3 = 12

Please let me know in case of any doubt.