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 |
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 −r1 | = | 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
Solution: 4!=24.
N!: This just calculates the factorial of N given by
GAM: This is the Gamma function which is defined by
Γ a=∫∞0 xa−1 e−x dx