Permutation & Combination Level-3 Quiz-1

1. The number of diagonals of a regular polygon is six times the number of its sides. How many sides does it have?

2. A committee of 5 is to be formed from 4 boys and 6 girls. In how many ways can it be formed if it consists of more boys than girls?

3. How many 4-letter words can be formed using letters A, B, C, D, E, F and G such that at least one letter of the word is a vowel?

4. In the above question, how many 7 letter words can be formed using these letters such that the letter at one of its ends is a vowel and that at the other end is a consonant?

5. In how many ways can a representation of 12 students consisting of 8 boys and 4 girls be selected from 15 boys and 10 girls, if a particular boy A and a particular girl B are never together in the representation?

6. If all the letters of the word ‘COCOCOLA’ are permuted in all possible ways and are arranged in a dictionary order, the what is the 561th word?

7. How many 9-digit multiples of 6 can be formed using only the digits 8 or 9?

8. A seven-digit number comprises of only 2’s and 3’s. How many of these are multiples of 12?

9. If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?

10. In how many ways can be select 5 cards from a card pack such that all 4 suits appear?