Find the number of words that can be formed by consider of thing all the possible permutations of the word FATHER. How many of these words begin with A and end with R.

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Solution

Solution :-
Given word : FATHER

(i) No. of letters = 6
Total ways are $6!$

(ii) No. of choice for $1^{s t}$ letter = 1(A)
No. of choice for last letter = 1(R)

Then remaining spaces can be filled in
$= 4 \times 3 \times 2 \times 1$ ways

$∴$ Total no. of ways $= 1 \times 4 \times 3 \times 2 \times 1 \times 1$

$= 24$ ways

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Find the number of words that can be formed by consider of thing all the possible permutations of the word FATHER. How many of these words begin with A and end with R.

Solution :-Given word : FATHER(i) No. of letters = 6Total ways are 6!(ii) No. of choice for 1st letter = 1(A)No. of choice for last letter = 1(R)Then remaining spaces can be filled in=4×3×2×1 ways∴ Total no. of ways =1×4×3×2×1×1=24 ways