Question

How many ways can 4 candy bars be chosen from a store that sells 30 candy bars (combination)

Answer 1

Using the combination formula (n!/(r!(n−r)!)), you would get a total of 27,405 combinations.

Answer 2

Answer:

Using the combination formula:

Number of combination of r object chosen from the total object i.e n is given by:

$\frac{n!}{r! \cdot (n-r)!}$

As per the statement:

4 candy bars be chosen from a store that sells 30 candy bars

Number of candy bars chosen from a store that sells 30 candy bars(r)= 4

and

Total candy bars(n) = 30

then substitute in the given formula we have;

$\frac{30!}{4! \cdot (30-4)!}$

⇒$\frac{30!}{4! \cdot (26)!}$

⇒$\frac{30 \cdot 29 \cdot 28 \cdot 27 \cdot 26!}{1 \cdot 2 \cdot 3 \cdot 4 \cdot (26)!}$

Simplify:

⇒$\frac{657720}{24} = 27,405$

therefore, 27,405  ways can 4 candy bars be chosen from a store that sells 30 candy bars