Question

1. For their uniforms, the Vikings soccer team has a choice of six different styles for the shirts, five for the shorts, and five colours for their socks. How many different uniforms are possible? A) 16 B) 150 C) 60 D) 55

2. The Niagara Ice Dogs have 4 people trying out for goal. Their coach wants to try a different goalie in each of the three periods of an exhibition game. In how many ways can the coach choose the three different goalies for the game? A) 12 B) 24 C) 7 D) 55 E) 20

3. How many arrangements of the word ALGORITHM begin with a vowel and end with a consonant? A) 18 B) 5040 C) 90720 D)181440 E) 362880

4. From a class of 14 boys and 9 girls, how many ways can I choose a committee of 6 to analyze classroom productivity with and equal number of boys and girls? A) 126 B) 252252 C) 30576 D) 448

5.A bag contains three green Christmas ornaments and four gold ornaments. If you randomly pick a single ornament from the bag, what is the probability that it will be green? A) 3/4 B)3/7 C)4/7 D)4/3

6. A bag contains three green Christmas ornaments and four gold ornaments. If you randomly pick two ornaments from the bag, at the same time, what is the probability that both ornaments will be gold?
A) 4/7 B) 2/7 C)3/7 D) none of the above

7. How many 4 digit number can be made using 0 -7 with no repeated digits allowed?
A) 5040 B) 4536 C) 2688 D) 1470

8. A coin is tossed three times. What is the probability of tossing three heads in a row?
A) 3/8 B)1/8 C)1/2 D)7/8

9. Two standard dice are rolled. What is the probability of rolling doubles (both the same number)?
A) 1/6 B)1/4 C)1/36 D) 5/36

10. There are 50 competitors in the men’s ski jumping. 30 move on to the qualifying round. How many different ways can the qualifying round be selected? A) 50! B) 30! C) 80 D) 1500 E) 1.25 × 1046

11. How many ways can the manager of a baseball team put together a batting order of his nine players, if the shortstop must bat 3rd?
A) 40320 B) 504 C) 362880 D) 120960

12. If a CD player is programmed to play the CD tracks in random order, what is the probability that it will play six songs from a CD in order from your favourite to your least favourite? A)1/6 B)2/3 C)1/720 D)5/6 E) 1/360

13. A group of eight grade 11 and five grade 12 students wish to be on the senior prom committee. The committee will consist of three students. What is the probability that only grade 12 students will be elected, assuming that all students have an equal chance of being elected?

Answer 1

We would be looking at the first 4 problems here as:

1) This is a case of multiplication rule:

Number of different uniforms possible is computed here as:
= Number of different shirts * Number of different shorts * Number of different socks

= 6*5*5

= 150

Therefore B)150 uniforms is the correct answer here.

2) There are 4 people possible here and we need to choose 3 different people for 3 different games. Therefore this is a case of permutation of 4 items taken 3 at a time. This is computed here as:

= 4! / (4 - 3)!

= 4! = 24

Therefore B) 24 is the number of ways here.

3) ALGORITHM

There are 3 vowels here: A, O and I
There are 6 consonants here: L, G, R , T, H, M

The first vowel can be chosen in 3 ways and last consonant in 6 ways.

Remaining we are left with 2 + 5 = 7 letters which can be permuted in 7! ways.

Therefore total number of arrangements possible here is computed as:
= 7!* 3*6

= 90720

ThereforeC) 90720 are the required number of arrangements here.

d) 14 boys and 9 girls, a committee of 6 members with equal number of boys and girls is computed here as:
= Number of ways to choose 3 boys from 14 boys * Number of ways to choose 3 girls from 9 girls

Therefore C) is the correct answer here.