a) FIND NUMBER OF DIFFERENT CODE CONSISTING OF 3 LETTERS FOLLOWED
BY 4 DIGITS THAT CAN BE OBTAINED FROM A,B,C,D 1,2,3,4,5,6?
If you cannot repeat letters or digits:
Choose the first letter 4 ways.
Choose the second letter 3 ways.
Choose the third letter 2 ways.
Choose the first digit 6 ways.
Choose the second digit 5 ways.
Choose the third digit 4 ways.
Choose the fourth digit 3 ways.
That's 4×3×2×6×5×4×3 = 8640
If you CAN repeat letters or digits:
Choose the first letter 4 ways.
Choose the second letter 4 ways.
Choose the third letter 4 ways.
Choose the first digit 6 ways.
Choose the second digit 6 ways.
Choose the third digit 6 ways.
Choose the fourth digit 6 ways.
That's 4×4×4×6×6×6×6 = 82944
b)FIND THE NUMBER OF 3-LETTER CODE WORDS THAT CAN BE MADE FROM
THE LETTERS A,P,P,L,E,S IF BOTH P's ARE USED?
That can be interpreted as
1. The two P's MUST be used
or
2. The two P's MAY be used.
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1. If the two P's MUST be used, there are 3 forms:
_PP, P_P, and PP_
And we can fill the blank 4 ways with A, L, E or S
That's 3×4 = 12 ways
2. If the two P's MAY be used, but don't have to be,
then in addition to those 12 ways, we can choose 3
letters from {A,P,L,E,S}
Choose the first letter 5 ways.
Choose the second letter 4 ways.
Choose the third letter 3 ways.
12 + 5×4×3 = 12 + 60 = 72 ways.
Edwin