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How many words can be formed with the letters of the word 'POSTMAN', if every word begins with T and ends with M?

How many words can be formed with the letters of the word 'POSTMAN', if every word begins with T and ends with M? Correct Answer 120

Concept:

If an object X can be chosen in 'a' ways and another object Y can be chosen in 'b' ways then the object X and Y can be chosen in 'ab' ways.

Calculation:

Here, there are 7 letters in the word "POSTMAN".

If we fix the first letter as T and the last letter as M then the arrangement would be like:

"T _ _ _ _ _ M"

Now we are left with 5 more letters.

The first blank space can be filled in 5 different ways by using any of the remaining letters. 

The second space can be filled in 4 different ways as one of the letters is already used to fill the first space.

Similarly, the third space can be filled in 3 different ways, the fourth in 2 different ways, and the last blank can only be filled with 1 way.

∴ Total number of ways in which we can arrange the letters = 5 × 4 × 3 × 2 × 1 = 120

Hence, the required answer is 120.

Related Questions

The following coding system shows the letter codes for numbers. Excluding the exceptions mentioned below, the digits in the question are to be transformed into letter codes as follows: Digit 0 1 2 3 4 5 6 7 8 9 Letter Code A B C D E F G H I J Exceptions: i. If a number begins with a nonzero even digit, that digit should be coded as N. ii. If a number begins with a nonzero odd digit, that digit should be coded as P. iii. If a number begins and also ends with non-zero even digits, those two digits at the extreme ends should be coded as Q. iv. If a number begins and also ends with nonzero odd digits, those two digits at the extreme ends should be coded as W. v. If a number's middle digit is a multiple of 2 that digit should be coded as Z. Barring these exceptions, the other digits should be codified as per the above-mentioned letter codes. Find the appropriate code for the following number-group 3214067
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The problem of perception can be compounded by the failure of parents and teachers to
Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
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