There is a group of 5 men, 6 women and 8 children. 1 man, 1 woman and one child are going to be selected to play a game. In how many ways can the selection be done?

Options

A. 480
B. 240
C. 120
D. 360

Answer

To solve the problem of selecting 1 man, 1 woman, and 1 child from a group of 5 men, 6 women, and 8 children, we can follow these steps:

### Step 1: Identify the number of choices for each category
- We have **5 men** to choose from.
- We have **6 women** to choose from.
- We have **8 children** to choose from.

### Step 2: Calculate the number of ways to select each category
- The number of ways to select **1 man** from 5 men is given by \(5C1\).
- The number of ways to select **1 woman** from 6 women is given by \(6C1\).
- The number of ways to select **1 child** from 8 children is given by \(8C1\).

### Step 3: Use the combination formula
The combination formula \(nCk\) is defined as \(nCk = \frac{n!}{k!(n-k)!}\). For \(k=1\), this simplifies to \(nC1 = n\). Therefore:
- \(5C1 = 5\)
- \(6C1 = 6\)
- \(8C1 = 8\)

### Step 4: Multiply the number of choices
To find the total number of ways to select 1 man, 1 woman, and 1 child, we multiply the number of choices:
\[ \text{Total Ways} = 5C1 \times 6C1 \times 8C1 = 5 \times 6 \times 8 \]

### Step 5: Calculate the total
Now, we calculate:
\[ 5 \times 6 = 30 \]
\[ 30 \times 8 = 240 \]

### Final Answer
Thus, the total number of ways to select 1 man, 1 woman, and 1 child is **240**.

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