For mathguru

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Math 30-1 Unit 6: Perms, Combs, Binomial Theorem Assignment

Name: _____________________________ /31 Marks

If your name does not appear in your writing on the hardcopy scan – you will lose one mark!

1. Determine the number of arrangements given the following requirements: (1 mark each)

a) The letters B, B, B, C, D, E, and O are arranged (all at once) in a row at random.

b) the 3 B's are together?

c) the 3 B"s are separated?

d) the first letter is B and the second letter is not B?

e) the first and last letters are vowels?

2. Determine the number of 5 person committees that can be created from 5 girls and 9 boys if,

(1 mark each)

a) No further restrictions.

b) 2 girls and 3 boys?

c) including a specific girl and excluding 2 specific boys?

d) all boys?

e) having at least 2 boys?

1

2

3. In how many ways can the letters of the word PERSON be arranged if the letters P and N

must be kept together? (1 mark)

4. How many numbers greater than 30 000 can be made from the digits 2, 3, 4, 5, 6 and 7?

(1 mark)

5. Simplify the following.

a) 5987!

5986! ( 1 mark)

(2 marks)

6. How many different ways can you get from point A to point B in each of the following?

(1 each)

a) b)

b) 2n 3

n 2

C

P

A

B

A

B

3

7. The number of vanity automobile license plates which can be made by using 6 letters followed

by 2 digits is given by n x 1010. The value of n is _______(nearest 100th and repetitions are

allowed). ( 1 mark )

8. Find the number of 5 card hands from a deck of 52 cards that have at least 2 aces. (1 mark)

9. Find the 7th term in the expansion of

9

2 1 2x

x

   

  . ( 2 marks)

10. If a regular polygon has 44 diagonals, find the number of sides. ( 2 marks )

11. If a football league consists of 10 teams, the number of league games played during the

season in which each team plays exactly three games with each of the other teams is _____.

(1 mark)

4

12. The numerical coefficient of the third degree term in the expansion of (2x – 1)5 is

( 2 marks)

13. The number of terms in the binomial expansion   k

2 2a 2

   

  is 11, then the value of ‘k’ is

( 2 marks)

14. The solution of the equation 4(n  2C2) = nC3 is

( 2 marks)

15. At a car dealership, the manager wants to line up 10 cars of the same model in the parking

lot. There are 3 red cars, 2 blue cars, and 5 green cars. If all 10 cars are lined up in a row facing

forward, determine the number of possible car arrangements if the blue cars cannot be together.

( 1 mark)