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in how many ways can letters of word ‘ARRANGEMENT’be arranged so that two ‘A’ and two ‘R’ does not comes together?

in how many ways can letters of word ‘ARRANGEMENT’be arranged so that two ‘A’ and two ‘R’ does not comes together?

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Geetesh
Total - {2Rs together + 2As together - RRAA all of them together}
.. beacuse both the cases where 2Rs/2As are together also include RRAA. We need to subtract those... Sort of Venn diagram problem
= 11!/(2!*2!*2!*2!) - {(2*10!/2!*2!2!) - 9!/2!*2! }
 Regards
ARUN (askIITians forum expert)

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