Passengers are to travel by a double decked bus which can accommodate 13 in the upper deck and 7 in the lower deck. Find the number of ways that they can be distributed if 5 refuse to sit in the upper deck and 8 refuse to sit in the lower deck.

A double-decker bus carry (u+l) passengers, u in the upper deck and l in the lower deck. Find the number of ways in which the u+l passengers can be distributed in the two decks, if r(lt=l) particular passengers refuse to go in the upper deck and s(lt=u) refuse to sit in the lower deck.

The number of ways in which a 7 people can sit around a round table is

Find the number of ways in which 5 distinct balls can be distributed in three different boxes if no box remains empty.

The number of ways in which 5 ladies and 7 gentlemen can be seated in a round table so that no two ladies sit together, is

Five boys and three girls are sitting in a row of 8 seats. Number of ways in which they can be seated so that not all the girls sit side by side is

The number of ways of choosing 5 cards out of a deck of 52 which include at least one king is

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

Find the number of ways in which 8 non-identical apples can be distributed among 3 boys such that every boy should get at least 1 apple and at most 4 apples.

The number of ways in which 7 people can sit around a table if two persons take consecutive seats is