from 6 different novels and 3 different dictionaries 4

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:

A. less than 500

B. at least 500 but less than 750

C. at least 750 but less than 1000

D. at least 1000

Answer : at least 1000

Solution :
∴ Required number of ways $$ =\,\, ^6{C_4} \times {\,^3}{C_1} \times 4!$$
$$ = 15 \times 3 \times 24 = 1080$$

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.

View Answer

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

View Answer

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

View Answer

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

View Answer

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:

Releted MCQ Question on
Algebra >> Permutation and Combination

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

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

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

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

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Permutation and Combination

Practice More MCQ Question on Maths Section

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:

Releted MCQ Question on Algebra >> Permutation and Combination

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

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

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

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

Practice More Releted MCQ Question on Permutation and Combination

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Algebra >> Permutation and Combination

Practice More Releted MCQ Question on
Permutation and Combination