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)** \(n=9, r=5\)