Advertisements
Advertisements
प्रश्न
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Advertisements
उत्तर
Total number of things = n
3 things must be together
∴ The number of remaining things = n – 3
Number of things to be selected = r
Out of r, 3 are always together
∴ Number of ways of selection = `""^(n - 3)"C"_(r - 2)`
Now permutation of 3 things which are always together = 3!
Number of permutations of (r – 2) things = (r – 2)!
∴ Total number of arrangements = `""^(n - 3)"C"_(r - 2) xx (r - 2)! xx 3!`
Hence the required arrangements = `""^(n - 3)"C"_(r - 2) xx (r - 2)! xx 3!`
APPEARS IN
संबंधित प्रश्न
Is 3! + 4! = 7!?
How many 4-digit numbers are there with no digit repeated?
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
Find x in each of the following:
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
