The number of ways to n people on circular table is (n-1)!
So, first we fix position of men, the number of ways to sit men = 5!
Now, women can sit in the gaps between men, there are 6 gaps between 5 mens,
So, women can sit in \(^6P_5\) ways
Hence, total number of ways = 5! x \(^6P_5\) = 5! x 6!
A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is
The number of ways of distributing 8 identical balls in 3 distinct boxes, so that none of the boxes is empty, is
How many ways are there to arrange the letters in the word ‘GARDEN’ with the vowels in alphabetical order ?
If the letters of the word ‘SACHIN’ are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number
At an election, a voter may vote for any number of candidates not greater than the number of candidates to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for atleast 1 candidate, then the number of ways in which he can vote is