Permutations And Combinations Question 23

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 [MP PET 1993]

Options:

A) 360

B) 900

C) 1260

D) 1620

Show Answer

Answer:

Correct Answer: B

Solution:

  • 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.