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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
William is 17 years old and Charmaine is 14 years old.
Step-by-step explanation:
Let x be the age of William and y be the age of Charmaine
Then
William is 3 years, older than Charmine.
x = y+3 Eqn 1
The sum of 3 times Charmaine's age and 2 times William's age is 76.
2x+3y = 76 Eqn 2
Putting x = y+3 in Eqn 2
Hence,
William is 17 years old and Charmaine is 14 years old.
Keywords: Linear equations, Variables
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