Question

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there?

a. 20

b. 7

c. 5!

d. 10

Answer 1

Answer: d. 10

Step-by-step explanation:

We know that the number of combinations of r objects selected from a group of n objects at a time is given by :-

$^nC_r=\dfrac{n!}{(n-r)!r!}$

Given : The total number of letters = 5

The number of letters need to select = 2

Then , the number of combinations of 2 letters selected from a group of 5 letters at a time is given by :-

$^5C_2=\dfrac{5!}{(5-2)!2!}=\dfrac{5\times4\times3!}{3!\times2}=10$

Hence, there are 10 possible selections.