H S Hall and S R Knight Solutions for Chapter: Permutations and Combinations, Exercise 2: EXAMPLES. XI. b.

In how many ways can the following prizes be given away to class of $20$ boys first and second classical, first and second mathematical, first science and first French?

A telegraph has $5$ arms and each arm is capable of $4$ distinct position including the position of rest, what is the total number of signals that can be made?

In how many ways can $7$ persons form a ring? In how many ways can $7$ English men and $7$ American sit down at a round table, no two Americans being together?

In how many ways, it is possible to draw a sum of money from a bag containing a sovereign, a half sovereign, a crown, a florin, a shilling, a penny and a farthing?

From $3$ coconuts, $4$ apples and two oranges, how many selections of fruit can be made, taking at least one of each kind.

Find the number of different ways of dividing $mn$ things into $n$ equal groups.

How many signals can be made by hoisting four flags of different colors, one above the other, when any of them are hoisted at once? Also, how many signals can be made with five flags?

Find the number of permutations which can be formed with the letters of the word '$\mathrm{series}$', taken three together.