91Ó°ÊÓ

There are two roads between towns \(\mathrm{A}\) and \(\mathrm{B}\). There are three roads between towns \(\mathrm{B}\) and \(\mathrm{C}\). How many different routes may one travel between towns \(\mathrm{A}\) and \(\mathrm{C}\).

How many ways can r different balls be placed in \(\mathrm{n}\) different boxes? Consider the balls and boxes distinguishable.

How many different numbers of 3 digits can be formed from the numbers \(1,2,3,4,5\) (a) If repetitions are allowed? (b) If repetitions are not allowed? How many of these numbers are even in either case?

Calculate the number of permutations of the letters \(\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\) taken four at a time.

In how many ways may a party of four women and four men be seated at a round table if the women and men are to occupy alternate seats?

How many different sums of money can be obtained by choosing two coins from a box containing a penny, a nickel, a dime, a quarter, and a half dollar?

How many baseball teams of nine members can be chosen from among I twelve boys, without regard to the position played by each member?

How many "words" each consisting of two vowels and three consonants, can be formed from the letters of the word "lintegral"?

Of 37 men and 33 women, 36 are teetotalers. Nine of the women are non-smokers and 18 of the men smoke but do not drink. 13 of the men and seven of the women drink but do not smoke. How many, at most, both drink and smoke.

Find the probability of drawing a black card in a single random draw from a well-shuffled deck of ordinary playing cards.