Question

List all the ways to select two members from S with repetition. The order in which the members are selected is not important. For example, DD is allowed and BA is the same vselection as AB.
S=[E,F,G,H,J]

Answer 1

Answer:

15 ways

Step-by-step explanation:

We are given that  a set S={E,F,G,H,J}

We have to find the number of ways to select two members from S with repetition.

Combination formula

$\binom{n}{r}=\frac{n!}{r!(n-r)!}$

We have n=5 , r= 2

Number of ways in which two members  from S can be selected when repetition is not allowed=$5C_2=\frac{5!}{2!(5-2)!}$

Number of ways in which two members  from S can be selected when repetition is not allowed=$\frac{5\times4\times3!}{2\times1 3!]$

Number of ways in which two members  from S can be selected when repetition is not allowed=$5\times 2=10$

When a member repeat then combination

{E,E},{F,F},{G,G},{H,H},{J,J}

There are 5 combination when a member is repeat and select two members from S.

Total number of ways in which to select two members from S with repetition =10+5=15 ways