Recall from Example 1 that whenever Suzan sees a bag of marb

Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, five green ones, four white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She has all the red ones.

Solution

Total marbles in bag = 14

Number of ways in which picking up 8 marbles out of which 4 are red marbles

= Number of ways of choosing 4 red marbles out of 4 red marbles * Number of ways of choosing 4 marbles out of the remaining 10 marbles

= 4C4*10C4 = 210

Total number of ways of picking up 8 marbles = 14C8 = 3003

Probability of picking up 8 marbles out of which 4 are red marbles = 210 / 3003 = 10/143