**Question 1: **How many one to one functions will be there from a set of five elements to the sets containing the following numbers.

a) 4

b) 9

c) 8

d) 5

** Solution: **

In a, b, c there will be no elements as the number of elements should be same in each set.

d) 5! = 120, the number of permutations having 5 elements.

**Question 2: **How many permutations does the letters ABCDEFG contain

a) The string EAC ?

b) The string CEF and ABC?

** Solution: **

a) A set of strings is M = { F, G, B, D, EAC } As the permutations comes upto 5 elements it will be 5! = 120.

b) The string M will be M = { ABCEF, D, G} . Here C will appear only once and M has 3 set of strings so it is 3! = 6.