A bag contains 3 one Rs coins, 4 five Rs coins and 5 ten Rs coins. How many selection of coins can be formed by taking atleast one coin from the bag

Answer

To solve the problem of how many selections of coins can be formed by taking at least one coin from the bag, we can follow these steps:

### Step 1: Identify the types and quantities of coins
We have:
- 3 coins of 1 Rs
- 4 coins of 5 Rs
- 5 coins of 10 Rs

### Step 2: Calculate the number of ways to select each type of coin
For each type of coin, we can choose from 0 up to the maximum number of coins available. The number of ways to select coins from each type can be calculated as follows:

- For 1 Rs coins: We can choose 0, 1, 2, or 3 coins. This gives us 4 options (0 to 3).
- For 5 Rs coins: We can choose 0, 1, 2, 3, or 4 coins. This gives us 5 options (0 to 4).
- For 10 Rs coins: We can choose 0, 1, 2, 3, 4, or 5 coins. This gives us 6 options (0 to 5).

### Step 3: Calculate the total number of selections including the option of selecting no coins
The total number of ways to select coins from all types (including the option of selecting no coins) is the product of the number of options for each type:
\[ \text{Total selections} = (3 + 1)(4 + 1)(5 + 1) = 4 \times 5 \times 6 \]

### Step 4: Perform the multiplication
Calculating the product:
\[ 4 \times 5 = 20 \]
\[ 20 \times 6 = 120 \]
So, the total number of selections including the option of selecting no coins is 120.

### Step 5: Subtract the selection of no coins
Since we need to find the number of selections that include at least one coin, we subtract the one case where no coins are selected:
\[ \text{Selections with at least one coin} = 120 - 1 = 119 \]

### Final Answer
Thus, the total number of selections of coins that can be formed by taking at least one coin from the bag is **119**.

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