HP 42S manual Probability, Where N!=N.N-1.N-2...2.1

4 Probability

Probability functions are in ▀ PROB menu (over x key).

They are COMB, PERM, N!, GAM, RAN and SEED.

COMB: This calculates the number of combinations of N things taken r at a time. The order does not matter. A thing cannot appear more than one time.

Example: If we have the five letters a, e, i, o and u the possible combinations taken one at a time are {a,e,i,o,u}. This means 5 combinations.

Taken two at a time

{ae, ai, ao, au, ei, eo, eu, io, iu, ou}. This means 10 combinations.

Taken four at a time

{aeio, aeiu, aeou, aiou, eiou}. This means also 10 combinations.

The number of combinations is given by

C  N , r =	N !	(Where N!=N.(N-1).(N-2)...2.1)
	r !  N −r !

To calculate this using 42S just enter N, press ENTER, enter r and press COMB.

PERM: This calculates the number of arrangements of N things taken r at a time. A thing cannot appear more than one time but now the order matters.

Example: Five cars are in a race. Their colors are red, blue, green, white and cyan. What are the possible results?

Solution: For the first position we have five possibilities. For the second position we have four possibilities, and three possibilities for the third position. So we have 5x4x3=60 different arrangements. To see this using 42S just enter 5, press ENTER, enter 3 and press PERM.

It is simple to realize that the number of arrangements is given by

A N , r =N. N −1 ... N −r1 = N !

N −r !

In particular if r=N (all the things are taken) then the arrangements are called permutations and the number of permutation is N!.

Example: In how many ways we can re-arrange the letters of the word “love”.

Solution: 4!=24.

N!: This just calculates the factorial of N given by N!=N.(N-1)...1 for a number (non-negative integer). The biggest number allowed is HP-42S is 253 and in Free42 is 170.

GAM: This is the Gamma function which is defined by

Γ a=∫∞0 xa−1 e−x dx