ITPEC FE Subject A April 2024 Question 2
Five people are sitting at a table in a restaurant. Two of them ordered coffee, and the other three ordered tea. The waiter forgets who ordered what and puts the drinks in a random order for the five persons. What is the probability that every person gets the correct drink?
Explanation
1/10 — only which two people get coffee matters, and exactly one such choice is correct.
The two coffees are identical, and so are the three teas, so an arrangement is fixed by choosing which 2 of the 5 people get coffee: C(5, 2) = 5 × 4 ÷ 2 = 10 equally likely outcomes.
Only one of them gives both coffees to the two coffee drinkers, and then the three teas land with the tea drinkers automatically. The probability is 1 ÷ 10.
Answer (c)
Why not others:
- •(a) 1/30 — would need 30 equally likely outcomes, but there are only 10 ways to place two identical coffees among five people
- •(b) 1/20 — counts ordered placements of the coffees, 5 × 4 = 20, but keeps a single favourable case; counted in order, the two coffee drinkers can receive them in 2 ways, giving 2 ÷ 20 again
- •(d) 3/10 — this is C(3, 2) ÷ 10, the chance that both coffees go to tea drinkers, a different event
Key rule: When items within a group are identical, count arrangements with combinations, and count the favourable cases the same way as the total.
Basic Theory · AI-written, may contain errors
This question comes from an official ITPEC past paper. ITPEC Practice is an independent study tool and is not affiliated with ITPEC. See the official FE past-paper collection or Report an issue.