Option 1 : \(\frac{5}{ 23}\)

**GIVEN:**

A piggy bank has 12, 5 and 7 coins of Rs. 10, Rs. 5 and Rs. 2 respectively.

**CONCEPT:**

Number of ways to select ‘a’ out of ‘b’ = ^{b}C_{a}

Probability = Number of favorable case / Total cases

**CALCULATION:**

Total coins = 12 + 5 + 7 = 24

2 coins are drawn at random:

Required probability = (^{12}C_{1} × ^{5}C_{1}) / (^{24}C_{2})

⇒ (12 × 5) / (276)

⇒ \(\frac{5}{ 23}\)