at an election a voter may vote for any number of

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is

A. 5040

B. 6210

C. 385

D. 1110

Answer : 385

Solution :
$$\eqalign{ & ^{10}{C_1}{ + ^{10}}{C_2}{ + ^{10}}{C_3}{ + ^{10}}{C_4} \cr & = 10 + 45 + 120 + 210 = 385 \cr} $$

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

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote 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

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote 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