Advertisements
Advertisements
प्रश्न
Evaluate each of the following:
8P3
उत्तर
8P3
nPr =\[\frac{n!}{(n - r)!}\]
∴ 8P3 =\[= \frac{8!}{(8 - 3)!}\]
\[ = 8 \times 7 \times 6 \]
\[ = 336\]
APPEARS IN
संबंधित प्रश्न
Is 3! + 4! = 7!?
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Which of the following are true:
(2 × 3)! = 2! × 3!
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
The number of five-digit telephone numbers having at least one of their digits repeated is
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
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
The number of arrangements of the word "DELHI" in which E precedes I is
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
The number of ways to arrange the letters of the word CHEESE are
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
If (n+2)! = 60[(n–1)!], find n
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Evaluate the following.
`(3! + 1!)/(2^2!)`
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
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?
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 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 different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
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 5-digit telephone numbers having atleast one of their digits repeated is ______.
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 ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
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! |
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.