How many words can be formed using the letter m 3 times letter p 4 times and the letter t 2 times

11.	In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Answer: Option A Explanation: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = 7 x 6 x 3 = 63. 2 x 1

13.

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

A. 10080 B. 4989600 C. 120960 D. None of these Answer: Option C Explanation: In the word 'MATHEMATICS', we treat the vowels AEAI as one letter. Thus, we have MTHMTCS (AEAI). Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different. Number of ways of arranging these letters = 8! = 10080. (2!)(2!) Now, AEAI has 4 letters in which A occurs 2 times and the rest are different. Number of ways of arranging these letters = 4! = 12. 2! Required number of words = (10080 x 12) = 120960.

How many words can be formed with all the letters of the word 'MISSISSIPPI' with or without meaning? 

1. 12250
2. 22500
3. 34650
4. 17500

Answer (Detailed Solution Below)

Option 3 : 34650

Free

Electric charges and coulomb's law (Basic)

10 Questions 10 Marks 10 Mins

Concept:

The number of ways to arrange n things taken all at a time out of which a thing is repeated r times is given by: n! / r!

Calculation:

Given: 'M I S S I S S I P P I'

There are 11 letters in the given word.

The letter 'I' is repeated 4 times in the given word.

The letter 'S' is repeated 4 times in the given word.

The letter 'P' is repeated 2 times in the given word.

As we know that, the number of ways to arrange n things taken all at a time out of which a thing is repeated r times is given by: n! / r!

∴ Number of words formed with all the letters of the given word 

 = 11! / (4!) × (4!) × (2!) = 34650

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