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

15 ways

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}=(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=(5!)/(2!(5-2)!)`

Number of ways in which two members from S can be selected when repetition is not allowed=

Number of ways in which two members from S can be selected when repetition is not allowed=
`5* 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