Combination of n Different Things Taken One or More at a Time

Q. Number of divisors of the form (4n + 2), n ≥ 0 of the integer 240 is ?

1. 4
2. 8
3. 10
4. 3

Q.

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:

(i) exactly 3 girls?
(ii) at least 3 girls?
(iii) almost 3 girls?

Q.

Eighteen guests have to be seated half on each side of a long table. Four particular guests desire to sit on one particular side and three on the other side.Determine the number of ways in which the sitting arrangements can be made.

Or

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw?

Q.

Number of divisors of n=38808 (except 1 and n) is

[RPET 2000]

1. 70

2. 68

3. 72

4. 74

Q.

How many words can be made out from the letters of the word ‘INDEPENDENCE’ in which vowels always come together?

1. $16800$

2. $16630$

3. $1663200$

4. $Noneofthese$

Q.

There are 60 students in a Mathematics class and 90 students in Physics class. Find the number of students which are either in Physics class or Mathematics class in the following cases.

(i) Two classes meet at the same hour.

(ii) Two classes meet at different hours and 30 students are enrolled in both the courses.

(iii) What value is shown here ?

Q.

Out of 10 white, 9 black and 7 red balls, the number of ways in which selection of one or more balls can be made, is_______.

1. 879

2. 892

3. 881

4. 891

Q.

The number of ways to put 6 letters in 6 addressed envelopes so that all are in wrong envelopes?

1. 9

2. 44

3. 264

4. 265

Q.

In an examination there are three multiple choice questions and each question has $4$ choices. Number of ways in which a student can fail to get all answers correct is?

1. $11$

2. $12$

3. $27$

4. $63$

Q. In the intermediate examination a candidate has to pass in each of the 6 subjects the number of ways that he can fail is

1. 60
2. 63
3. 61
4. 62

Q.

The number of ways in which a mixed double game can be arranged from amongst $5$ married couples if no husband and wife play in the same game is

1. $56$

2. $60$

3. $96$

4. None of these

Q.

The letters of the word ASHISH are permuted and are arranged in an alphabetical order as in an English dictionary. Then, the rank of the word ASHISH is _____

___

Q.

The total number of ways of dividing 15 different things into groups of 8, 4 and 3 respectively is

1. 

2. 

3. 

4. 

Q.

How many words with or without meaning, each 2 of vowels and 3 consonants can be formed from the letters of the word DAUGHTER? In the today's society, we see that many parents don't want girl child and get the abortion before the birth. What values is violated by the parents?

Q. $150$ workers were engaged to finish a job in a certain number of days.$4$ workers dropped out on second day, $4$more workers dropped out on third day and so on. It took $8$ more days to finish the work. Find the number of days in which the work was completed.

Q. Number of divisors of the form (4n + 2), n ≥ 0 of the integer 240 is ?

1. 8
2. 10
3. 4
4. 3

Q. Find the degree measures corresponding to the following radian measures $(Use\pi =\frac{22}{7})$.
(i) $\frac{11}{16}$
(ii) $-4$
(iii) $\frac{5\pi }{3}$
(iv) $\frac{7\pi }{6}$

Q. Sum of proper divisors of the number $1260$ is

Q.

There are 15 students in a class, out of which a team of 9 players is to be formed. If the captain always remains the same, we have to select x players from y students. Find the value of x + y.

1. 19

2. 20

3. 22

4. 25

Q. If the number of arrangements of letters of the word $DHARAMSHALA$ taken all at a time so that no two alike letters appear together is $4^a\cdot 5^b\cdot 6^c\cdot 7^d,$ where $a,b,c,d\in N,$ then the value of $a+b+c+d$ is

Q.

Team of four students is to be selected from a total of 12 students for a quiz competition. In how many ways it can be selected if two particular students do not wish to be together in the team.

1. 495

2. 450

3. 

4. 420

Q. If $N$ is the number of ways in which a person can walk up a stairway which has $7$ steps if he can take $1$ or $2$ steps up the stairs at a time, then the value of $N/3$ is

Q.

Team of four students is to be selected from a total of 12 students for a quiz competition. In how many ways it can be selected if two particular students refuse to be together and two particular students wish to be together only in the team. .

1. 240

2. 210

3. 260

4. 226

Q.

Team of four students is to be selected from a total of 12 students for a quiz competition. In how many ways it can be selected if two particular students have to be included in the team.

1. 12

2. 

3. 

4. 

Q.

Team of four students is to be selected from a total of 12 students for a quiz competition. In how many ways it can be selected if two particular students wish to be included together only.

1. + 45

2. 45

3. 

4. + 45

Q. If $\frac{a+b{e}^y}{a-b{e}^y}=\frac{b+c{e}^y}{b-c{e}^y}=\frac{c+d{e}^y}{c-d{e}^y}$ , then a, b, c, d are in

1. HP
2. AP
3. GP
4. None of these

Q. A man has $3$ friends. The number of ways he can invite one friend everyday for dinner on $6$ successive nights so that no friend is invited more than $3$ times is $N$, then $N/170$

Q.

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

Q. Let S = {1, 2, 3, ………, 9}. For k = 1, 2, ……..5, let $N_k$ be the number of subsets of S, each containing five elements out of which exactly k are odd. Then $N_1+N_2+N_3+N_4+N_5=$

1. 210
2. 252
3. 126
4. 125

Q. In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?