Things of beauty part1

Find the number of selections of one or more things from the group of p identical things of one type, q identical things of another type, r identical things of the third type and n different things.

Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If she is not beautiful, then I will not marry her.

A movie theater is 3 blocks due north of a supermarket, and a beauty parlor is 4 blocks due east of the movie theate. How many blockes long is the steet that runs directly from the supermarket to the beauty parlor?

Cell the unit of life part 1

If an angle alpha be divided into two parts such that the ratio of tangents of the parts is K. If x be the difference between the two parts , then prove that sinx = (K-1)/(K+1) sin alpha .

Assertion. Linnaeus insisted that the scientific names should be latinized. Reason. This gives beauty to the names.

A bomb at rest explodes into two parts of masses m_(1) and m_(2) . If the momentums of the two parts be P_(1) and P_(2) , then their kinetic energies will be in the ratio of:

The number of ways in which m+n(nlem+1) different things can be arranged in a row such that no two of the n things may be together, is

Show that the total number of permutations of n different things taken not more than r at a time, when each thing may be repated any number of times is (n(n^(r)-1))/((n-1)) .

Statement 1: If p ,q ,ltr , the number of different selections of p+q things taking r at a time, where p thingks are identical and q other things are identical, is p+q-r+1. Statement 2: If p ,q ,>r , the number of different selections of p+q things taking r at a time, where p thingks are identical and q other things are identical, is r-1.