# Need Help on Probability of Combination

#### Sarmmer

##### New member
Hi everyone, this is my first thread here.

where
p + q + r = 100%
x + y + z = n

#### Sarmmer

##### New member
It is commonly known to have the first equation for Probability of Combination (Success & Failure)

However, I have a situation where there are 3 types of outcomes (eg. win, lose and tie).
Please share your thoughts if it shall be done in other ways. Thank you.
P, p, q, r = probability
n = number of ways event can occurs
x, y, z = targeted outcome

#### Dr.Peterson

##### Elite Member
Hi everyone, this is my first thread here.
View attachment 26412

where
p + q + r = 100%
x + y + z = n
This is not very clearly stated; but the formula at the top is for the binomial distribution, which gives the probability of getting x successes in n random trials, each with probability p for success and q of failure.

The formula at the bottom does give the probability of x wins, y losses, and z ties out of n trials with respective probabilities p, q, r.

It is commonly known to have the first equation for Probability of Combination (Success & Failure)

However, I have a situation where there are 3 types of outcomes (eg. win, lose and tie).
Please share your thoughts if it shall be done in other ways. Thank you.
P, p, q, r = probability
n = number of ways event can occurs
x, y, z = targeted outcome
This is still not stated quite right, though it is better. n is not the number of ways an event can occur, but the number of trials. x, y, and z are the number of each of the three outcomes in those n trials.

See https://en.wikipedia.org/wiki/Multinomial_distribution

#### Sarmmer

##### New member
Hi Dr. Peterson, thank you for the clarification and sharing the reference.