SATHEE: Permutations And Combinations Question 49

Permutations And Combinations Question 49

Question: The number of different words that can be formed out of the letters of the word ‘MORADABAD’ taken four at a time is

Options:

A) 500

B) 600

C) 620

D) 626

Show Answer

Answer:

Correct Answer: D

Solution:

In MORADABAD, we have 6 different types of letters $ 3A^{s} $ , $ 2D^{s} $ and rest four different. We have to form words of 4 letters. (i) All different $ ^{6}P_4=6\times 5\times 4\times 3=360 $ . (ii) Two different two alike $ ^{2}C_1{{\times }^{5}}C_2\times \frac{4\ !}{2!}=240 $ (iii) 3 alike 1 different $ ^{1}C_1{{\times }^{5}}C_1\times \frac{4\ !}{3\ !}=20 $ (iv) 2 alike of one type and 2 alike of other type $ ^{2}C_2\times \frac{4\ !}{2\ !\ 2\ !}=6 $ Therefore total number of words $ =360+240+20+6=626 $ .

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Permutations And Combinations Question 49

Question: The number of different words that can be formed out of the letters of the word ‘MORADABAD’ taken four at a time is

Options:

Answer:

Solution:

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