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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 !
r !N −r!
(Where N!=N.(N-1).(N-2)...2.1)
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 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
∞
x
a−1
e
−x
dx