→ (r), → (p), → (q), → (s)

Sol.

Required number of ways = (2 + 1) (3 + 1) (4 + 1) – 1 = 59.

10 C 3 = 120

Requied number of ways = Coefficient of x 10 in (1 + x + x 2 + ......) 4

= Coefficient of x 10 in (1 – x) –4 = 10+4–1 C 4–1 = 13 C 3 = 286

The word ‘MATHEMATICS’ consists of 11 letters of which 7 are consonants namely M,M, T, T,H,C,S and 4 vowels and a group of consonants can be

arranged in ways. ( ∴ A is repeated twice)

In any such arrangement, seven consonants can be reshuffled among themselves in

ways. (  Either of M and T is repeated twice)

Hence, the required number of ways = = = 75600.

──────────────────────────────────────────────────────────────────────────────────────────