1. Two mating fruit flies each have one gene for black eyes and one for red eyes. The offspring receive one eye-colour gene from the male and one from the female.

a)Produce a tree diagram showing all the possible combinations for the offspring.

b)How many distinct combinations can be produced?

2. There are 14 members in a student government. They decide to send a committee of 3 students, one of who will be designated as the spokesperson, to negotiate a new attendance policy with the principal.

a)In how many ways can this be done?

b)Suppose there are 8 women and 6 men in the student government. How many possibilities are there if the committee must have at least 1 person of each gender?

3.How many 8-letter sequences are there consisting of As, Bs, and Cs with the following restrictions?

c)The sequence must have exactly 4 A’s.

d)The sequence must have exactly 3 A’s and 3 B’s.