Discussion

Answer: B

We need to count the number of factors of 5 in the product of all odd numbers from 1 to 99. The multiples of 5 in this product are 5, 15, 25, 35, 45, 55, 65, 75, 85, 95.

Let's count the factors of 5 from each term:

5 = \(1 \times 5\) (one 5)

15 = \(3 \times 5\) (one 5)

25 = \(5 \times 5\) (two 5s)

35 = \(7 \times 5\) (one 5)

45 = \(9 \times 5\) (one 5)

55 = \(11 \times 5\) (one 5)

65 = \(13 \times 5\) (one 5)

75 = \(3 \times 25 = 3 \times 5 \times 5\) (two 5s)

85 = \(17 \times 5\) (one 5)

95 = \(19 \times 5\) (one 5)

Total number of factors of 5 is \(1+1+2+1+1+1+1+2+1+1 = 12\).