In a class of 45 pupils ,21 play chess , 23 play cards and 5 play both the games . Find
how many do not play any of the games,

Answer

To solve the problem step by step, we will use the principle of inclusion-exclusion.

### Step 1: Identify the total number of pupils and those who play games
- Total number of pupils = 45
- Number of pupils who play chess = 21
- Number of pupils who play cards = 23
- Number of pupils who play both chess and cards = 5

### Step 2: Calculate the number of pupils who play at least one game
To find the total number of pupils who play at least one game, we can use the formula:
\[ \text{Number of pupils who play at least one game} = (\text{Number who play chess}) + (\text{Number who play cards}) - (\text{Number who play both}) \]
Substituting the values:
\[ \text{Number of pupils who play at least one game} = 21 + 23 - 5 \]

### Step 3: Perform the calculation
Now let's calculate:
\[ 21 + 23 = 44 \]
Then subtract the number of pupils who play both:
\[ 44 - 5 = 39 \]
So, 39 pupils play at least one game.

### Step 4: Calculate the number of pupils who do not play any games
To find the number of pupils who do not play any games, we subtract the number of pupils who play at least one game from the total number of pupils:
\[ \text{Number of pupils who do not play any games} = \text{Total pupils} - \text{Number who play at least one game} \]
Substituting the values:
\[ \text{Number of pupils who do not play any games} = 45 - 39 \]

### Step 5: Perform the final calculation
Now let's calculate:
\[ 45 - 39 = 6 \]
Thus, the number of pupils who do not play any games is 6.

### Final Answer
The number of pupils who do not play any of the games is **6**.

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