Question

1. How many 12-digit phone numbers can be created with the following restrictions:

a) no restrictions

b) first number cannot be zero or one.

c) no repeated numbers

2. Find the number of distinguishable permutations of the letters in the following words.

a) CALCULUS

b) PEPPER

c) MISSISSIPPI

Answer 1

1. a) The number of 12-digit phone numbers can be created without any restrictions = [Since, each digit can be any one of the 10 digits, so total possibilities are (10 * 10 *....12 times)]. (Ans).

b) Since, first number can't be 0 or 1, it will be any one of the remaining 8 digits and the remaining 11 digits can be any one of the 10 digits. Hence, total number of possibilities = 8 * . (Ans).

c) Since, there are 10 digits and we have to create 12 digit phone number, it is not possible to create a phone number without any repeated numbers. (Ans).

2. a) There are 2 C's, 2 L's, 2 U's, 1 A and 1 S in CALCULUS.

So, total number of distinguishable permutations of the letters = = 5040 (Ans).

b) There are 3 P's, 2 E's and 1 R in PEPPER.

So, total number of distinguishable permutations of the letters = = 60 (Ans).

c) There are 1 M, 4 I's, 4 S's, 2 P's in MISSISSIPPI.

Hence, total number of distinguishable permutations of the letters = = 34,650 (Ans).