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

## Trending Questions

**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

- 220
- 220+1
- 221
- 220−1

**Q.**How many 3×3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of MTM is 5?

- 126
- 198
- 162
- 135

**Q.**

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

5880

7560

5!

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

- 360
- 114
- 72
- 54

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

- 192
- 148
- 176
- 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

- 1680
- 1698
- 2436
- 2454

**Q.**

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

$4!$

$3!\times 4!$

$7!$

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?

$24800$

$25100$

$25200$

$25400$

**Q.**

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

120

240

720

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

- 120
- 270
- 264
- 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

- 37
- 7C3
- None of these
- 73

**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?

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

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

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

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

**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:

$96$

$144$

$512$

$576$

**Q.**Consider the word ′′SUCCESS′′, then the total number of possible words

- when all the letters are taken at a time is 420
- when All S′s are not together is 360
- when no two S′s are together is 180
- 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

- 63360
- 63300
- 63260
- 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.

- c>a>b
- c>b>a
- a+b+c=460×6!
- a+c=91b

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

- 4
- 2
- 5
- 8

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

- 100
- 720
- 120
- 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

- 1560
- 1080
- 480
- 840

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

- 1440
- 240
- 360
- 720