Advertisements
Advertisements
Question
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
Advertisements
Solution
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
RELATED QUESTIONS
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
The number of ways to arrange the letters of the word CHEESE are
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
Evaluate the following.
`(3! + 1!)/(2^2!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
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 the first four questions have three choices and the remaining have five choices?
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
The total number of 9 digit numbers which have all different digits is ______.
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
