Question

In Exercises 17 – 22, use the counting principle to determine the number of possible outcomes of each experiment.
17. Two digits are selected from the digits 1, 2, 3, 4, and 5, where the same digit can be used twice.

21. Four-digit telephone extensions are generated, where the first digit cannot be a 0, 1, 8, or 9.

Answer 1

17) Repetition is allowed as same digit can be used twice.

Total ways to fill first place = 5

Total ways to fill second place = 5

Hence total two digits numbers = 5*5 = 25

21) Total digits = 10 and repetition is allowed in telephone extensions.

First digit can be fill by 10 - 4 = 6 ways (as we cannot take 0, 1, 8 and 9)

Second, third and fourth digits can be filled by 10 ways (as no restrictions for these)

Total telephone extensions = 4*10*10*10 = 4000

Please comment if any doubt. Thank you.