# Permutations and Combinations Questions - Permutation and Combinations

16:

In the above problem, if the first digit cannot be 0, then

 A. 42100 B. 421200 C. 42400 D. 421600 Option: B Explanation : n=26x 25x 9x 9x 8=421200.
17:

In how many ways can 10 people be seated in a row so that a given pair is not next to each other?

 A. 10 ! - 9 ! B. 10! - 2(9!) C. 9! D. none of these Option: B Explanation :
18:

The number of ways to cut a six sided convex polygon whose vertices are labeled into four triangles using diagonal lines that do not cross is

 A. 13 B. 14 C. 12 D. 11 Option: C Explanation :
19:

Suppose a licence plate contains two letters followed by three digits with the first digit not zero. How many different licence plates can be printed?

 A. 608000 B. 608200 C. 608400 D. 608600 Option: C Explanation : Each letter can be printed in twenty-six different ways, the first digit in nine ways and each of the other two digits in ten ways. Hence 26 x 26 x 9 x 10 x 10 = 608400 different plates can be printed.
20:

Given  nPr =  3024

Value of n will be

 A. 3 B. 4 C. 6 D. 9 Option: D Explanation : Sinnce is product of consecutive positive integers Hence npr = 3024 = 9 x 8 x 7 x 6 Hence,         n = 9