Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
How many numbers between 100 and 1000 have the digit 7 exactly once?
A teacher wants to select the class monitor in a class of 30 boys and 20 girls. In how many ways can the monitor be selected if the monitor must be a girl or a boy?
A Signal is generated from 2 flags by putting one flag above the other. If 4 flags of different colours are available, how many different signals can be generated?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is 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 numbers between 100 and 1000 have 4 in the units place?
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
A school has three gates and four staircases from the first floor to the second floor. How many ways does a student have to go from outside the school to his classroom on the second floor?
How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 5 if digits are not repeated?
Select the correct answer from the given alternatives.
A college has 7 courses in the morning and 3 in the evening. The possible number of choices with the student if he wants to study one course in the morning and one in the evening is -
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.
In how many ways 5 persons can be seated in a row?
A mobile phone has a passcode of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the passcode?
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 not allowed
How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed
How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is allowed
Count the numbers between 999 and 10000 subject to the condition that there are no restriction
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 allowed?
How many strings can be formed using the letters of the word LOTUS if the word either starts with L or ends with S?
Count the total number of ways of answering 6 objective type questions, each question having 4 choices
In how many ways 10 pigeons can be placed in 3 different pigeon holes?
Find the value of `(("n" + 3)!)/(("n" + 1)!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 10, r = 3
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 5 digit numbers all digits of which are odd i
The number of ways in which a garland can be formed by using 10 identical pink flowers and 9 identical white flowers is ______
How many numbers are there between 99 and 1000 having atleast one of their digits 7?
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 ______.
A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing question
The number of six-digit numbers, all digits of which are odd is ______.
Three letters can be posted in five letterboxes in 35 ways.
The number of all four digit numbers which begin with 4 and end with either zero or five is ______.
