Q. 94.0( 2 Votes )
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together.
6 men can be arranged in (6-1)! = 5! ways to dine at a round table.
Now, if we place 5 women in 6 empty seats between them so that no two women will be together, and this can be done in 6P5 ways i.e. in
As, the operations are dependent, so, the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together.
The discussion can be shown pictorially as:
[X = 6 empty seats between the 6 men(M)]
Rate this question :
Which of the following are true :
(2 + 3)! = 2! + 3!RD Sharma - Mathematics
Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?RD Sharma - Mathematics
. There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?RD Sharma - Mathematics
How many permutations can be formed by the letters of the word, ‘VOWELS,’ when
all vowels come together?RD Sharma - Mathematics
Find the total number of ways in which six ‘+’ and four ‘-‘ signs can be arranged in a line such that no two ‘-‘ signs occur together.RD Sharma - Mathematics
In how many ways can the letters of the word “INTERMEDIATE” be arranged so that :
i. the vowels always occupy even places?
ii. the relative order of vowels and consonants do not alter?RD Sharma - Mathematics
From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?RD Sharma - Mathematics
How many different words can be formed with the letters of word ‘SUNDAY’? How many of the words begin with N? How many begin with N and end in Y?RD Sharma - Mathematics
How many three-digit numbers are there, with distinct digits, with each digit odd?RD Sharma - Mathematics
In how many ways can five children stand in a queue?RD Sharma - Mathematics