Question

Problem 6 Apply each of the four counting/sampling methods (with replacement and with ordering, without replacement and with ordering, without replacement and without ordering, and with replacement and without ordering) to a unique situation that correspond to your interests or your studies. For each of your four example situations, note the value of n, the value of k, and the total number of possible combinations.

Answer 1

Answer:

Example;

In Riya's birthday party there are 10 friends are came and Riya has 5 chocolate only to distribute her friends.

(i).

Consider these 5 chocolate are of same type and she don't want to give any friend more than one chocolate.

(a).

Here situation is Without replacement and Un-ordered.

Here n=10 k=5

Total number of possible combinations=

(ii).

Consider these 5 chocolates are of same type but she are willing to give some friend more than one chocolate.

With replacement & un-ordered

Here n=10 , k=5

Total number of possible combinations=

(iii).

Consider 5 chocolate are of different type & she don't want to give any friend more than one chocolate.

Without replacement & Ordered

Here n=10,k=5

Total number of possible combinations=P_kⁿ=P₅¹⁰=30240

(iv)

Consider 5 chocolate are of different type & she is willing to give some friend more than one chocolate.

With replacement & Ordered

Here n=10,k=5

Total number of possible combinations=n^k=10⁵=100,000

If we are using with replacement that means one friend can be comes more than one time in the sample.

i.e, We can select one friend to give chocolate more than one time. Means we are giving more chocolate to one friend.

Here order of chocolate means, if there are different type of chocolate. Consider for example,

Mango flavor and strawberry and suppose that two friends selected are tam & Shyam. Then Ordering affect means.

Mango Ram

Strawberry Shyam

9's not same as;

Mango Shyam

Strawberry Ram