Q1: Consider the word BASKETBALL

Question

a) how many of the arrangements begin with a k? (60 480)

b) how many of the arrangements start with a B and end with a K? (10 080)

For this question, I am not sure what they mean but it beginning with k or b...

Q2: Joanne's bag of marbles contain one red, three blue and four green marbles. If she reaches in to select some without looking, how many different arrangements could she make? (39)

I feel that I have the most trouble understanding the question so I don't know how to start...

Answer 1

you have
BB
AA
LL
E
T
K
S

start with K
= 1x9!/(2!2!2!) = 45360

( I think you divided by 3 times 2!)

b) BxxxxxxxxK
number = 8!/(2!2!)
= 10080
(you had that one right, the other B is now just one of the guys)

Q2: A bit tricky.
e.g. she could take them all, she could take 3 greens and 2 blue or .....

there is one red
she can take the red in 2 ways:
- don't take it, take 1

there are 3 blues
she can take the blues in 4 ways,
- don't take it, take 1, take 2, or take all three

there are 4 green
she can take the greens in 5 ways,
- dont't take it, take 1, .....

Number of ways to take marbles
= 2(4)(5) = 40 ways

but that includes the case of not taking a red, not taking a blue and not taking a green.
It says she took "some" so we will subtract that 1 case

Number of ways to select marbles = 40-1 = 39

Answer 2

@reiny thank you!