Statistics - Combination with replacement

Each of several possible ways in which a set or number of things can be ordered or arranged is called permutation Combination with replacement in probabipty is selecting an object from an unordered pst multiple times.

Combination with replacement is defined and given by the following probabipty function −

Formula

${^nC_r = frac{(n+r-1)!}{r!(n-1)!} }$

Where −

${n}$ = number of items which can be selected.

${r}$ = number of items which are selected.

${^nC_r}$ = Unordered pst of items or combinations

Example

Problem Statement −

There are five kinds of frozen yogurt: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. What number of varieties will there be?

Solution −

Here n = 5 and r = 3. Substitute the values in formula,

${^nC_r = frac{(n+r-1)!}{r!(n-1)!} \[7pt] = frac{(5+3+1)!}{3!(5-1)!} \[7pt] = frac{7!}{3!4!} \[7pt] = frac{5040}{6 imes 24} \[7pt] = 35}$

Statistics - Combination with replacement

Formula

Example

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