A family consisting of an old man, 6 adults and 4 children, is to be seated in a row for dinner. The children wish to occupy the two seats at each end and the old man refuses to have a child on either side of him. In how many ways can the seating arrangement be made for the dinner?
If all the permutations of the letters of the word CHALK be written down as in a dictionary, what is the rank of the word?
There are six students of whom 2 are Indians, 2 Americans and the remaining 2 are Russians. They have to stand in a line so that the two Indians are together, the two Americans are together and so also the two Russians. Show that there are 48 different ways of arranging the students.
A cricket team is to be formed consisting of 2 wicket keepers, 4 bowlers and 5 batsmen form a group of players containing 4 wicket keepers, 8 bowlers and 11 batsmen. Find the number of ways a cricket team can be constituted.
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further in how many of these committees
- a particular professor is included?
- a particular student is excluded?
In how many ways can 21 white balls and 19 black balls be arranged in a row so that no two black balls may be together?