## Permutation and Combination

Q1. How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

Ans: 504

Q2. How many 4-digit numbers are there with no digit repeated?

Ans: 4536

Q3. How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

Ans: 60

Q4. Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repeated. How many of these will be even?

Ans: 120, 48

Q5. **Find r if**

**(i) ^{5}P_{r} = 2^{6}P_{r-1} **

Ans: 3

**(ii) ^{5}P_{r} = ^{6}P_{r-1}**

Ans: 4

Q6. How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

Ans: 40230

Q7. In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?

Ans: 33810

Q8. **If ^{n}C_{8} = ^{n}C_{2}, find ^{n}C_{2.}**

Ans: 45

Q9. **Determine n if ^{2n}C_{3:}^{n}C_{3} = 12: 1**

Ans: 5

Q10. Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

Ans: 2000

Q11. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Ans: 778320