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)⁵P_r = 2⁶P_r-1 

Ans: 3

(ii) ⁵P_r = ⁶P_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 ⁿC₈ = ⁿC₂, find ⁿC_2.

Ans: 45

Q9. Determine n if ²ⁿC_3:ⁿC₃ = 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