Advertisements
Advertisements
Question
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
Advertisements
Solution
Arrangement of 4 women sitting at 4 even places = 4! = 24
Ways to seat 5 men at 5 odd places = 5! = 120
Arrangement of 4 women to sit at even places and 5 men to sit at odd places
= 4! x 5!
= 24 x 120
= 2880
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
Prove that
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
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?
Twelve students complete in a race. In how many ways first three prizes be given?
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many three-digit odd numbers are there?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?
If 18Cx = 18Cx + 2, find x.
If 8Cr − 7C3 = 7C2, find r.
If n +2C8 : n − 2P4 = 57 : 16, find n.
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular professor is included.
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
If 20Cr = 20Cr + 4 , then rC3 is equal to
If C (n, 12) = C (n, 8), then C (22, n) is equal to
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Find the value of 15C4
Find the value of 80C2
Find the value of 15C4 + 15C5
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
15C8 + 15C9 – 15C6 – 15C7 = ______.
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?
