Combination of r Things from n Things When All Are Not Different

Q. There are $15$ players in a cricket team, out of which $6$ are bowlers, $7$ are batsmen and $2$ are wicketkeepers. The number of ways, a team of $11$ players be selected from them so as to include at least $4$ bowlers, $5$ batsmen and $1$ wicketkeeper, is

Q.

The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is

Q. The number of ways of choosing $10$ objects out of $31$ objects of which $10$ are identical and the remaining $21$ are distinct, is

1. $2^{20}$
2. $2^{20}+1$
3. $2^{21}$
4. $2^{20}-1$

Q. How many $3\times 3$ matrices $M$ with entries from $\{0,1,2\}$ are there, for which the sum of the diagonal entries of $M^{T}M$ is $5?$

1. $126$
2. $198$
3. $162$
4. $135$

Q.

Find the number of permutations of the letters of the word ALLAHABAD.

1. 5880

2. 7560

3. 5!

4. 9!

Q.

Find the number of 5 letter words, with or without meaning, which can be formed out of the letters of the word MARIO , where the repetition of the letters is not allowed ___ .

Q.

Find the number of ways in which 8 distinct toys can be distributed among 5 children.

Q.

Find the number of combinations and permutations of $4$ letters taken from the word 'EXAMINATION'.

Q. All the letters of the word ‘EAMCET’ are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is

1. 360
2. 114
3. 72
4. 54

Q. Number of words that can be formed by using the $4$ letters of the word $MISSISSIPPI$ is

1. $192$
2. $148$
3. $176$
4. $164$

Q. Number of words that can be formed by taking $4$ letters at a time out of the letters of the word $MATHEMATICS$ is

1. $1680$
2. $1698$
3. $2436$
4. $2454$

Q.

The number of words which can be formed from the letters of the word MAXIMUM, if two consonants cannot occur together, is

1. $4!$

2. $3!\times 4!$

3. $7!$

4. None of these

Q.

Out of $7$ consonants and $4$ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2$ vowels, is equal to?

1. $24800$

2. $25100$

3. $25200$

4. $25400$

Q.

The number of ways to arrange the letters of the word Cheese are

1. 120

2. 240

3. 720

4. 6

Q.

Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other ?

Q. Messages are conveyed by arranging $4$ white, $1$ blue and $3$ red flags on a pole. Flags of the same colour are alike. If a message is transmitted by the order in which the colours are arranged, the total number of messages that can be transmitted if exactly six flags are used is

Q. The number of $4$ letter words (with or without meaning) that can be made from the eleven letters of the word "EXAMINATION" is

Q. The number of four letter words that can be formed using the letters of the word $BARRACK$ is

1. $120$
2. $270$
3. $264$
4. $144$

Q. There are 3 candidates for a post and one is to be selected by the votes of 7 men. The number of ways in which votes can be given is

1. $3^7$
2. ${}^7{C}_3$
3. None of these
4. $7^3$

Q. Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together.

Q.

The number of ways of arranging the letters $\text{AAAAABBBCCCDEEF}$ in a row when no two $\text{Cs}$ are together is?

1. $\frac{15!}{5!3!3!2!}-3!$

2. $\frac{15!}{5!3!3!2!}-\frac{13!}{5!3!2!}$

3. $\frac{12!}{5!3!2!}\times \frac{{}^{13}{P}_3}{3!}$

4. $\frac{12!}{5!3!2!}\times {}^{13}{P}_3$

Q. 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 is

Q.

The number of permutations by taking all letters and keeping the vowels of the word COMBINE in odd places is equal to:

1. $96$

2. $144$

3. $512$

4. $576$

Q. Consider the word ${}^{\prime \prime }SUCCES{S}^{\prime \prime }$, then the total number of possible words

1. when all the letters are taken at a time is $420$
2. when All $S^{\prime }s$ are not together is $360$
3. when no two $S^{\prime }s$ are together is $180$
4. taking $4$ letters at a time is $92$

Q. There are 12 pairs of shoes in a box. Then the possible number of ways of picking 7 shoes so that there are exactly two pairs of shoes are

1. 63360
2. 63300
3. 63260
4. 63060

Q. Words are formed using all letters of the word 'JEEADVANCED'.
Let $a$ denotes the number of words in which all the vowels are together.
Let $b$ denotes the number of words in which vowels as well as consonants are separated.
Let $c$ denotes the number of words which begin and end with vowels.

1. $c>a>b$
2. $c>b>a$
3. $a+b+c=460\times 6!$
4. $a+c=91b$

Q. The class marks of a distribution are $6,10,14,18,22,26,30$ then the class size is

1. 4
2. 2
3. 5
4. 8

Q. The number of three digit numbers of the form xyz where x > y > z is

1. 100
2. 720
3. 120
4. 600

Q. The total number of $6$ digit numbers that can be made using digits $1,2,3,4$, if all the digits should appear in the number at least once is

1. $1560$
2. $1080$
3. $480$
4. $840$

Q. Number of ways of selecting $6$ shoes, out of $6$ pair of shoes, having exactly two pairs is

1. $1440$
2. $240$
3. $360$
4. $720$