# Lecture 1 Permutations and Combinations

Look in the mirror. That’s your competition.

# Lecture - 1 Chapter 7 Permutations and Combinations

 NCERT Exercise 7.1

Fundamental Principle of Counting

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?

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?

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?

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?

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

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?

 NCERT Exercise 7.2

Question 1. Evaluate
(i) 8!
(ii) 4! – 3!

Question 2. Is 3! + 4! = 7!?

Question 3. Compute $\frac{8!}{6! \times 2!}$

Question 4. If $\frac{1}{6!}+\frac{1}{7!} = \frac{x}{8!}$, find x.

Question 5. Evaluate $\frac{n!}{(n-r)!}$, when
(i) $n=6, r=2$
(ii) $n=9, r=5$