Chapter 7 – Permutations and Combinations (Ex – 7.1)

Permutations and Combinations (Ex – 7.1)

Question 1.
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?

Solution.
(i)

(ii) When repetition is not allowed then first place can be filled in 5 different ways, second place can be filled in 4 different ways & third place can be filled in 3 different ways. Therefore by the multiplication principle the required number of three digit numbers is 5 x 4 x 3 i.e, 60.

Question 2.
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Solution.

Question 3.
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Solution.

Question 4.
How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Solution.

Question 5.
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Solution.
When a coin is tossed there are two possible outcomes i.e. head or tail. When the coin is tossed three times then the total possible outcomes are 2 x 2 x 2 i.e., 8.

Question 6.
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

Solution.