Answer:
Using the combination formula:
Number of combination of r object chosen from the total object i.e n is given by:
[tex]\frac{n!}{r! \cdot (n-r)!}[/tex]
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;
[tex]\frac{30!}{4! \cdot (30-4)!}[/tex]
⇒[tex]\frac{30!}{4! \cdot (26)!}[/tex]
⇒[tex]\frac{30 \cdot 29 \cdot 28 \cdot 27 \cdot 26!}{1 \cdot 2 \cdot 3 \cdot 4 \cdot (26)!}[/tex]
Simplify:
⇒[tex]\frac{657720}{24} = 27,405[/tex]
therefore, 27,405 ways can 4 candy bars be chosen from a store that sells 30 candy bars
There are 27,405 ways to choose 4 candy bars from a store that sells 30 candy bars.
To find the ways to choose we will use selection method( Combination)
Combination refers to selection of items or anything we will find the ways by using formula of combination.
[tex]{}_^n \mathrm{ C }_r =\frac{n!}{r!(n-r)!}[/tex] r objects chosen from n object at a time.
According to the Combination formula,
Now, given that 4 candy bars be chosen from total 30 candy bars so we will simplify by putting the value of n and r in the formula and evaluate,
[tex]= \frac{30!}{4!(30-4)!}\\\\= \frac{30!}{4!(26)!}\\\\= \frac{30\times 29\times 28\times 27 \times 26!}{4\times 3\times 2\times 1(26)!}\\\\\rm On simplifying we get,\\\\=\frac{657720}{24}\\\\=27,405[/tex]
Therefore, There are 27,405 ways to choose 4 candy bars from a store that sells 30 candy bars.
Learn more about Permutations and Combinations here : https://brainly.com/question/2943700
