How many "words" can be written using exactly five a's and no more than three b's (and no other letters)?

This is a problem of Permutations. We have 3 cases depending on the number of B's. Since no more than three B's can be used we can use either one, two or three B's at a time.

Case 1: Five A's and One B

Total number of letters = 6

Total number of words possible =

Case 2: Five A's and Two B's

Total number of letters = 7

Total number of words possible =

Case 3: Five A's and Three B's

Total number of letters = 8

Total number of words possible =

Total number of possible words will be the sum of all three cases.

Therefore, the total number of words that can be written using exactly five A's and no more than three B's (and no other letters) are 6 + 21 + 56 = 83

84

Step-by-step explanation

Case 1: Five A's and One B

Total number of letters = 6

Total number of words possible = 6

Case 2: Five A's and Two B's

Total number of letters = 7

Total number of words possible = 21

Case 3: Five A's and Three B's

Total number of letters = 8

Total number of words possible = 56

Case 4: Five A's and no B's

Total number of letters = 5

Total number of words possible = 1

Total number of possible words will be the sum of all three cases.

Therefore, the total number of words that can be written using exactly five A's and no more than three B's (and no other letters) are 1+6 + 21 + 56 = 84

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

it is true

step-by-step explanation:

all the combinations add up i used   calculator