Advertisements
Advertisements
Question
Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.
Advertisements
Solution
We have 2 women and 3 men
First women choose the chairs amongst the chairs 1 to 4
i.e. Total number of chairs = 4
So, the number of arrangements = 4P2 ways
Now 3 men choose from the remaining 6 chairs
So, the number of arrangements = 6P3 ways
∴ Total number of arrangements = 4P2 × 6P3
= `(4!)/((4 - 2)!) xx (6!)/((6 - 3)!)`
= `(4!)/(2!) xx (6!)/(3!)`
= `(4*3*2!)/(2!) xx (6*5*4*3!)/(3!)`
= 12 × 120
= 1440
Hence, the total number of possible arrangements are 1440.
APPEARS IN
RELATED QUESTIONS
How many numbers between 100 and 1000 have 4 in the units place?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?
In a test, 5 questions are of the form 'state, true or false'. No student has got all answers correct. Also, the answer of every student is different. Find the number of students appeared for the test.
How many four digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
Select the correct answer from the given alternatives.
A college offers 5 courses in the morning and 3 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening
Answer the following:
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?
Three persons enter into a conference hall in which there are 10 seats. In how many ways they can take their seats?
Given four flags of different colours, how many different signals can be generated if each signal requires the use of three flags, one below the other?
Four children are running a race:
In how many ways can the first two places be filled?
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is allowed
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is not allowed
Count the numbers between 999 and 10000 subject to the condition that there are no restriction
Count the numbers between 999 and 10000 subject to the condition that there are at least one of the digits is repeated
How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition of digits are not allowed?
To travel from a place A to place B, there are two different bus routes B1, B2, two different train routes T1, T2 and one air route A1. From place B to place C there is one bus route say B1, two different train routes say T1, T2 and one air route A1. Find the number of routes of commuting from place A to place C via place B without using similar mode of transportation
How many numbers are there between 1 and 1000 (both inclusive) which are divisible neither by 2 nor by 5?
How many strings can be formed using the letters of the word LOTUS if the word neither starts with L nor ends with S?
Find the value of 4! + 5!
Find the value of 3! – 2!
Find the value of 3! × 2!
Find the value of `(12!)/(9! xx 3!)`
Find the value of n if (n + 1)! = 20(n − 1)!
Find the value of n if `1/(8!) + 1/(9!) = "n"/(10!)`
Choose the correct alternative:
The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is
Choose the correct alternative:
The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is
Choose the correct alternative:
The number of 5 digit numbers all digits of which are odd i
How many numbers are there between 99 and 1000 having 7 in the units place?
In how many ways can this diagram be coloured subject to the following two conditions?
(i) Each of the smaller triangle is to be painted with one of three colours: red, blue or green.
(ii) No two adjacent regions have the same colour.
There are four bus routes between A and B; and three bus routes between B and C. A man can travel round-trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, in how many ways can he make round trip?
In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answer correct is ______.
Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point
Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.
Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated.
In a steamer there are stalls for 12 animals, and there are horses, cows and calves (not less than 12 each) ready to be shipped. They can be loaded in 312 ways.
