In how many ways can the letters of the word ldquo arrange rdquo be arranged so that neither two As ...........

Quantitative Aptitude ( CCS) Permutation & Combination

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In how many ways can the letters of the word “arrange” be arranged so that neither two As nor two Rs come together?

1640

1740

660

1840

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Explanation:

Total no of arrangements possible=7!/2!2!=1260
Total no of arrangements in which Rs are together=6!/2!=360
Total no of arrangements in which 2 As are together=6!/2!=360
Total no of arrangements in which 2 As as well as 2 R’so are together= 5!=120
Therefore total no. of arrangements in which neither 2 As nor 2 Rs are together= 1260-360-360+120=660