Permutations Question

[ErionK]

Hello all, I've tried doing this question that I've listed below. I started and finished part a, but im unsure if i have the correct answer. I am also unsure how to begin part b so if someone could help i would appreciate it! The question is listed below. THANK YOU!!!!! <3

How many ways can you arrange the letters BASKETBALL if:

a) the arrangement must begin with an S and end with a T?

b) all of the vowels must be kept together?

 

[Qwertyuiop[]]

Hello all, I've tried doing this question that I've listed below. I started and finished part a, but im unsure if i have the correct answer. I am also unsure how to begin part b so if someone could help i would appreciate it! The question is listed below. THANK YOU!!!!! <3
View attachment 33422
How many ways can you arrange the letters BASKETBALL if:

a) the arrangement must begin with an S and end with a T?

b) all of the vowels must be kept together?

Why don't you write BASKETBALL instead of using numbers like I've done? Also there is repetition because you have 2 LL in basketball.

EDIT: I forgot you have 2 BB as well. So 4 repetition in total.

 

[tri]

For a)
Account for the repeats of BB, LL, AA by dividing by 2!2!2!
For b)
Take all the vowels together as a single letter (of which there are 3 possibilities), and see what words you can make with these 8 letters.

 

[Dr.Peterson]

Hello all, I've tried doing this question that I've listed below. I started and finished part a, but im unsure if i have the correct answer. I am also unsure how to begin part b so if someone could help i would appreciate it! The question is listed below. THANK YOU!!!!! <3
View attachment 33422
How many ways can you arrange the letters BASKETBALL if:

a) the arrangement must begin with an S and end with a T?

b) all of the vowels must be kept together?

We can restate the first problem: How many ways can you arrange the letters BAKEBALL? (or BBAALLKE)

We have two Bs, two As, and two Ls, so you can't just think of it as arranging 8 distinct letters, as you are doing.

Have you learned a formula or method for solving that sort of problem, where the letters to be arranged include duplicates?