Advertisements
Advertisements
प्रश्न
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
Advertisements
उत्तर
Number of men = 3
Number of coats = 4
Number of waist coats = 5
Number of caps = 6
4 coats can be given to 3 men in 4P3 ways.
5 waist coats can be given to 3 men in 5P3 ways.
6 caps can be given to 3 men in 6P3 ways.
∴ Total number of ways of wearing 3 coats, 4 waist coats and 6 caps is
= 4P3 × 5P3 × 6P3
= `(4)/((4 - 3)!) xx (5!)/((5 - 3)!) xx (6!)/((6 - 3)!)`
= `(4!)/(1!) xx (5!)/(2!)xx (6!)/(3!)`
= `(4 xx 3 xx 2 xx 1)/1 xx (5 xx 4 xx 3 xx 2 xx 1)/(2 xx 1) xx (6 xx 5 xx 4 xx 3!)/(3!)`
= 24 × 6 × 120
= 1,72,800
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
How many 4-digit numbers are there with no digit repeated?
Find r if `""^5P_r = ""^6P_(r-1)`
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
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?
In how many ways can 5 different balls be distributed among three boxes?
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 arrangements of the word "DELHI" in which E precedes I is
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
Find x if `1/(6!) + 1/(7!) = x/(8!)`
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:
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
What is the maximum number of different answers can the students give?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
