Question

6. Determine the number of divisors for 12 600 that are divisible by three. Use the fact that a divisor of a number is the multiplication of one or more factors of the number. (T)

10. Two students are selected at random from a group consisting of 5 girls and 3 boys. Determine the probability that both students are girls given that at least one is a girl. (K)

Answer 1

6)

Let d(n) be the number of divisors for the natural number, n.

We begin by writing the number as a product of prime factors: n = (p^a)(q^b)(r^c)...

then the number of divisors, d(n) = (a+1)(b+1)(c+1)...

So 12600 = (2^3)*(3^2)*(5^2)*7

Hence the number of divisors will be 4*3*3*2 which is 72. Ans

10) Given that atleast one girl is selected, the required probability will be to select one girl from remaining 4 girls and 3 boys.

Hence the required probability will be 4/7 ~ 0.5714 Ans