Question

Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

A. 69760

B. 30240

C. 99784

D. None of these

Answer : 69760

Solution :
Total number of words that can be formed $$= {10^5}$$
Number of words in which no letter is repeated $$=\, ^{10}{P_5}.$$ So, number of words in which at least one letter is repeated $$ = {10^5} - {\,^{10}}{P_5} = 69760.$$

Releted MCQ Question on
Algebra >> Permutation and Combination

Releted Question 1

$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:

A. 1

B. 2

C. 3

D. None of these.

Releted Question 2

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are

A. 69760

B. 30240

C. 99748

D. none of these

Releted Question 3

The value of the expression $$^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}{C_3}} $$ is equal to

A. $$^{47}{C_5}$$

B. $$^{52}{C_5}$$

C. $$^{52}{C_4}$$

D. none of these

Releted Question 4

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

A. $$^6{C_3} \times {\,^4}{C_2}$$

B. $$^4{P_2} \times {\,^4}{C_3}$$

C. $$^4{C_2} + {\,^4}{P_3}$$

D. none of these

Practice More Releted MCQ Question on
Permutation and Combination