What is the unit digit in the expansion of (57242)9×7×5×3×1 ?

• The expression is the product of the first 9 odd numbers: 1 × 3 × 5 × 7 × 9 × 11 × 13 × 15 × 17.

• To find the unit digit of the product, we only need to consider the unit digits of the individual factors: 1, 3, 5, 7, 9, 1, 3, 5, 7.

• The product includes the factor 5 (from the number 5 and 15) and the factor 3 (from the number 3, 13, etc.).

• Any integer ending in 5 multiplied by any odd integer ending in 3, 7, or 9 will result in a unit digit of 5 (e.g., 5 × 3 = 15, 5 × 7 = 35, 5 × 9 = 45).

• Since the product contains at least one factor ending in 5 and all other factors are odd, the final unit digit must be 5.

• However, looking at the options provided (2, 4, 6, 8), none is 5. Re-evaluating the question text: 'What is the unit digit in the expansion of (57242)9×7×5×3×1 ?' The notation is ambiguous. If it means (57242)^(9*7*5*3*1), the base ends in 2. The exponent is 945 (odd). 2^1=2, 2^2=4, 2^3=8, 2^4=16. The cycle is 2,4,8,6. Since 945 is odd, 945 mod 4 = 1. The unit digit is 2. This matches option (a).