Given, word ATRAPATRAM Here, A→4 times T→2 times R→2 times P→1 time M→1 time (i) All A's are together, Then it will be consider as one letter and remaining 6 letters and 1′A′s (including 4A′s )will be consider as 7 letters. ∴ Number of arrangement =
7!
2!2!
=x . . . (i) (ii) no two A′ s are together. such that −T−R−P−T−R−M− ∴ Number of arrangement =7C4×