A person put a garland holiday decor with 25 bulbs that are placed in a series c

Question

A person put a garland holiday decor with 25 bulbs that are placed in a series circuit (The Garland stops working when one or more of the 25 bulbs fuse). The Garland stops working and one person examines and informs him that the Garland has four (4) fused bulbs but, he don't says were they are. The person takes four (4) new bulbs (functioning) to replace the fused bulbs, decide to do it at random and removed four (4) of the 25 bulbs and replaced them .

A) In how many different ways could that person select four (4) bulbs of the garland that he will replace?

B) In how many different ways could that person select four (4) bulbs that he will replace in such a way that none of the four (4) bulbs selected are fused ?

C) In how many different ways could that person select four (4) bulbs that will be replaced in such a way that only two (2) of the four (4) are fused ?

D) What is the probability that the person fix the Garland after selecting four (4) random bulbs and replaced with new bulbs ?

Explanation / Answer

a)

number of ways = 25C4 = 12650

b)

number of ways = 21C4 = 5985

c)

number of ways = 4C2 * 21C2 = 1260

d)

probability = 4C4/25C4 = 1/12650

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