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

The correct option is B

900

The word ARRANGE, has AA,RR, NGE letters. That is two A' s, two R's and N, G, E one each.
$\therefore$The total number of arrangements $\frac{7!}{2!2!1!1!1!}$=1260
But, the number of arrangements in which both RR are together as one unit = $\frac{6!}{2!1!1!1!1!}$ = 360
$\therefore$The number of arrangements in which both RR do not come together = 1260 - 360 = 900.