Answer:
b) 36
Step-by-step explanation:
We can use combinations to solve this problem.
The binomial coefficient [tex]\binom{n}{k}=\frac{n!}{k!(n-k)!}[/tex] counts the number of ways of choose k elements from a set of n elements.
The product rule from combinatorics says that if there are N ways of doing something and M ways of doing another thing, the number of ways of doing both things is equal to NM.
First, we choose the blue balls. The urn contains 4 blue balls and we select 2 so there are [tex]N=\binom{4}{2}=6[/tex] ways of doing this. Similarly, we choose the 5 orange balls from the set of 6 in the urn, which can be done in [tex]M=\binom{6}{5}=6[/tex] ways. By the product rule, there are MN=6(6)=36 ways of selecting all the balls.
The number of ways 2 blue balls and 5 orange balls can be selected from the urn is 36 number of ways: Option C is correct
Combination has to do with selection.
If r number is selected from n number, this is expressed using the formula:
[tex]nC_r=\frac{n!}{(n-r)!r!}\\[/tex]
If 2 blue balls are selected from 4 blue balls, this is expressed as:
[tex]4C_2=\frac{4!}{(4-2)!2!}\\4C_2=\frac{4\times 3 \times 2!!}{2!2!}\\4C_2=\frac{12}{2} = 6 ways[/tex]
Similarly, if 5 orange balls are selected from 5 orange balls, this is expressed as:
[tex]6C_5=\frac{6!}{(6-5)!5!}\\6C_5=\frac{6\times 5!}{1!5!}\\6C_5=\frac{6}{1} = 6 ways[/tex]
The number of ways 2 blue balls and 5 orange balls can be selected from the urn is 36 number of ways
Learn more here: https://brainly.com/question/23589217
