Question

9) How many four letter word can be 1 point
formed using a, b, c, d and e with
repetition
*
O 120
O
24
O 16
O 625​

Answer 1

Step-by-step explanation:

(i) There are 6 different letters in the word MONDAY.

Number of 4-letter words that can be formed from the letters of the word MONDAY, without repetition of letters, is the number of permutations of 6  different objects taken 4 at a time, which is 6P4.

Thus, required number of words that can be formed using 4 letters at a time is

6P4=(6−4)!6!=2!6!=2!6×5×4×3×2!=6×5×4×3=360

(ii) There are 6 different letters in the word MONDAY. 

The first place can be filled in 6 ways.

Second place can be filled by any one of the remaining 5 letters. So, second place can be filled in 5 ways

Third place can be filled by any one of the remaining 4 letters. So, third place can be filled in 4 ways

So, on continuing, number of ways of filling fourth place in 3 ways , fifth place in 2 ways, six place in 1 way.

Therefore, the number of words that can be formed using all the letters of the word MONDAY, using each letter exactly once is 6×5×4×3×2×1=6!

Alternative Method:

Number of words that can be formed by using all the letters of the word MONDAY at a time is the number of permutation of 6 different objects taken 6 at a time, which is 6P6=6!

Thus, required number of words that can be formed when all letters are used at a time= 6!=6×5×4×3×2×1=720

(iii) Total number of letters in the word MONDAY is 6.

Number of vowels are 2(O,A)

Six letters word is to be formed.

□□□□□□

First letter should be a vowel. So, the rightmost place of the words formed can be filled only in 2 ways.

Since the letters cannot be repeated , the second place can be filled by the remaining 5 letters. So, second place can be done in 5 ways

Similarly, third place in 4 ways , fourth place in 3 ways, fifth place in 2 ways, sixth place in 1 way.

Hence, required number of words that can be formed using four letters of the given word is 2×5×4×3×2×1=240