The document contains several word problems involving combinations and permutations: 1) There are 9 women and 8 men in a room, and a committee of 5 needs to be chosen with at least 4 women. The number of ways this can be done is calculated. 2) If 5 people are randomly chosen from the same group to form a committee, the probability that there will be at least 4 women is calculated to 3 decimal places. 3) The number of 3-digit numbers that can be formed using the digits 0-9 without repetition and with the second digit even is calculated. The calculations for each problem are briefly explained.

1. There are 9 women and 8 men in a room.
a) Five of them will be chosen to form a committee. How many ways can the
members of this committee be chosen if it must contain at least 4 women?
b) If five of the people are chosen at random to form a committee, what
is the probability that there will be at least 4 women on this committee?
Give your answer correct to 3 decimal places.

2. Using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, how many 3-digit numbers can
be made if there are no repetitions of digits and the second digit is even?
Briefly explain your calculations.

3. In how many ways can 7 students be seated in a row if Hi and Lois, two of
the students, must sit next to each other?

4. The term occurs in the expansion of .
The value of n is:

5. There are 12 athletes to be separated into 3 teams of 4.
The Sabres choose their players, then the Tigers and finally the Lions.
In how many ways can this be done?

6. A grad committee of 4 students is to be selected from a class of 24
students. Annie, Betty and Connie decide that they do not want to be on
the committee.
How many different committees are possible? Express your answer in
factorial notation.

7. A father wishes to have a picture taken with his 4 sons.
In how many different ways can they line up for the picture if the father
must stand in the middle?