Advertisements
Advertisements
Question
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
Advertisements
Solution
There are 6 men and 8 women.
To make all 6 men together treat them as 1 unit.
Now there are 1 + 8 = 9 persons.
They can be arranged in 9! ways.
After this arrangement the 6 men can be arranged in 6! ways.
So total number of arrangement = 9! × 6!
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?
Find r if `""^5P_r = 2^6 P_(r-1)`
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
Which of the following are true:
(2 × 3)! = 2! × 3!
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
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?
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?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
Find x if `1/(6!) + 1/(7!) = x/(8!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
