Question

In how many ways can the letter of the word FATHER be arranged to form the words beginning with A ending with H

Answer 1

Step-by-step explanation:

• There are 6 letters in the word FATHER.

• “You want H to appear right next to T”

• Lets tie up H & T together so as they appear as one unit, i.e. TH.

• Now, you have got 5 letters(or different items), i.e., F, A, TH, E, R, which can be arranged in 5! ways.

• So your answer should be 5! = 120.

Answer 2

Given :  Word FATHER

To Find :  in how many  Ways  letters can be arranges from FATHER to form the word beginning with A not ending with H

Solution:

F A  T H E  R

Total Number of Letters  = 6

word beginning with A

Hence 1st Letter is Fixed as

A x  x  x  x  x

Remaining 5 Letters

Last letter can not be  H

Hence Last position can be filled in 4 Ways   ( F T E R )

Now  4 Letters  lefts and 4 positions left

Hence 4 !  = 24  Ways

Total Ways  =   4 * 24  = 96

in 96 Ways  letters can be arranges from FATHER to form the word beginning with A not ending with H

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