Question

How many permutations exist of the letters a, b, c, d taken two at a time?

a. 12
b. 8
c. 2

Answer 1

The number of permutations of the 4 different letters, taken two at a time, is given by:

`4P2=(4!)/(2!)=12`

Answer 2

Answer: The correct option is (a) 12.

Step-by-step explanation: We are given to find the number of permutations that exists for the letters a, b, c and d taking two at a time.

We know

The number of permutations of 'n' different things taking 'r' ('r' less than or equal to 'n') at a time is given by the formula:

`^nP_r=(n!)/((n-r)!).`

In the given case, there are 4 different letters and we are to take two at a time, so

n = 4 and r = 2.

Therefore, the number of permutations will be

`^4P_2=(4!)/((4-2)!)=(4!)/(2!)=(4*3*2* 1)/(2* 1)=4* 3=12.`

Thus, there are 12 permutations that exists.

Option (a) is correct.