Question

The number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is

• A. 360
• B. 900
• C. 1260
• D. 1620

Answer 1

Answer: (C)

1260

Answer 2

The word ARRANGE, has AA, RR, NGE letters, that is two A' s, two R's and N, G, E one each.

∴The total number of arrangements

= $\frac { 7 ! } { 2 ! 2 ! 1 ! 1 ! 1 ! 1 ! }$ = 1260

But, the number of arrangements in which both RR are together as one unit = $\frac { 6 ! } { 2 ! 1 ! 1 ! 1 ! 1 ! }$ = 360.

The number of arrangements in which both RR do not come together = 1260 – 360 = 900.