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?
a) The sequence must have at least one A.
b) The sequence must have at least one of each symbol.
c) The sequence must have exactly 4 A’s.
d) The sequence must have exactly 3 A’s and 3 B’s.
4. A necklace is made out of identically shaped, coloured beads. Ten beads are red, 9 are black, 7 are white, 12 are pink, and 4 are purple. The beads are strung together on a waxed string. The ends are tied together to form a large knot that prevents the beads from sliding past it. How many different necklaces can be made in this way?