Advertisements
Advertisements
प्रश्न
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Advertisements
उत्तर
Each of the six men can be arranged amongst themselves in 6! ways.
The five women can be arranged amongst themselves in the six places in 5! ways.
∴ By fundamental principle of counting, total number of ways = 6! x 5!
APPEARS IN
संबंधित प्रश्न
Compute `(8!)/(6! xx 2!)`
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Find n if n – 1P3 : nP4 = 1 : 9
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
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?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Evaluate each of the following:
8P3
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
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 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
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
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
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
If (n+2)! = 60[(n–1)!], find n
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?
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The possible outcomes when a coin is tossed five times:
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
The total number of 9 digit number which has all different digit is:
The number of ways to arrange the letters of the word “CHEESE”:
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
How many ways can the product a2 b3 c4 be expressed without exponents?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are 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 ______.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur 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 ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
