Advertisements
Advertisements
प्रश्न
Evaluate each of the following:
8P3
Advertisements
उत्तर
8P3
nPr =\[\frac{n!}{(n - r)!}\]
∴ 8P3 =\[= \frac{8!}{(8 - 3)!}\]
\[ = 8 \times 7 \times 6 \]
\[ = 336\]
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many 4-digit numbers are there with no digit repeated?
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Find x in each of the following:
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 numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
In how many ways can 7 letters be posted in 4 letter boxes?
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA 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 6 men can be arranged in a row so that three particular men are consecutive, is
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! + 1!)/(2^2!)`
The number of ways to arrange the letters of the word “CHEESE”:
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
Find the distinct permutations of the letters of the word MISSISSIPPI?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
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 distinct things taken r together, in which 3 particular things must occur together.
The total number of 9 digit numbers which have all different digits is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
