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These are three different questions from permutations. How many four letter words can be formed from MATHEMATICS INFINITE PHYSICS

These are three different questions from permutations.
How many four letter words can be formed from
  1. MATHEMATICS
  2. INFINITE
  3. PHYSICS                                                   

Grade:11

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
8 years ago
For Mathematics

M-2
A-2
T-2
H-1
E-1
I-1
C-1
S-1
( 8 different letters)
So following cases are possible for 4 letter words
2 doublets
(Out of M,A,T) 2 can be chosen in 3C2 ways and then arrange in(4!/2!2!) ways

1 doublet 2 different
Out of 3 doublets 1 can be chosen in 3C1 way and remaining 2 letters from 7 choices in 7C2 ways and then arranged in 4!/2! ways i.e 3C1*7C2* (4!/2!) ways

all 4 different
This is simple 4 letters to be chosen from 8different choices in 8P4 ways

Add all three cases to get final ans. Similarly you can do for other words as well.

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