Question

Your mother went to budgetwise to buy the following: coffee (C), milk (M), sugar
(S), and butter (B).
Upon reaching the grocery department, she found out that her money is just enough to buy any three of these items. In how many ways can she select the three items? List the possible selections.​

Answer 1

Answer:

she will buy a milk to budgetwise

Explanation:

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Answer 2

There are 4 ways to choose three items to buy.

1. Coffee (C), Milk (M), and Sugar (S)
2. Coffee (C), Milk, and Butter (B)
3. Coffee(C), Sugar (S), and Butter (B)
4. Milk (M), Sugar(S), and Butter (B)

Step-by-Step Explanation:

Given set of items:

Coffee (C)

Milk (M)

Sugar(S)

Butter (B)

Total number of items = 4 = n

Concept:

Given N number of items, the number of ways we can make a set of p objects is given by the formula $N \choose p$

Formula used:

$N \choose p = \tfrac{N!}{p!(N-p)!}$

Here, $N$ represents the total number of items available

          $p$ represents the number of objects to be chosen.

Steps:

• There are total 4 objects - coffee (C), milk (M), sugar (S), and butter (B). Hence, $N =4$
• Mother has to buy any three of these, so she has to choose 3. Hence, $p = 3$
• So, the number of ways for her to select the three items is $N \choose p$
• Substituting the real values in the formula, we get
  $N \choose p = 4 \choose 3$
• Upon solving this, we get
  $4 \choose 3 = \tfrac {4!}{3! (4-3)!}$
• Further simplification gives us
  $4 \choose 3 = \tfrac {4!}{3!1!} = \tfrac {4!}{3!} = 4$

So, there are exactly 4 ways mother can select three items. The four ways are:

1. Coffee (C), Milk (M), and Sugar (S)
2. Coffee (C), Milk, and Butter (B)
3. Coffee(C), Sugar (S), and Butter (B)
4. Milk (M), Sugar(S), and Butter (B)