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.

Find the number of ways in which 6 boys and 6 girls can be seated in a row so that all the girls sit together and all the boys sit together.

The number of ways in which 7 persons can be seated at a round table if twom particular persons are not to sit together is

Find the number of ways in which 6 men and 5 women can dine at around table if no two women are to sit so together.

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

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.

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Find the probability distribution of the number of aces.

Column I, Column II The number of five-digit numbers having the product o digit 20 is, p. > 70 A closest has five pairs of shoes. The number of ways in which four shoes can be drawn from it such that there will be no complete pair is, q. <60 Three ladies have each brought their one child for admission to a school. The principal wants to interview the six persons one by one subject to the condition that no mother is interviewed before her child. The number of ways in which interview can be arranged is, r. in (50 ,110) The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is, s. in (40 ,70)

A monochromatic light of wavelength 500 nm is incident normally on a single slit of width 0.2 mm to produce a diffraction pattern. Find the angular width of the central maximum obained on the screen. Estimate the number of fringes obatined in Young's double slit experiment with fringe width 0.5 mm, which can be accommodated within the region of total angular spread of the central maximum due to single slit.

In how many ways can a committee of a 3 ladies and 4 gentlemen be appointed from a meeting consisting of 8 ladies and 7 gentlemen ? What will be the number of ways if Mrs . X refuses to serve in a committee if Mr . Y is a member