ITPEC FE Subject A October 2025 Question 3
ITPEC FE Subject A October 2025 — Question 3 of 60
Probability of adjacent seating — count favorable outcomes using the block method.
Three friends must sit together in a row of 7 seats.
- •Total outcomes:
7!=5040 - •Favorable outcomes:
- •Treat 3 friends as one block →
5possible starting positions (seats 1–5) - •Friends permute within the block:
3!=6 - •Remaining 4 people permute:
4!=24 - •Total:
5 × 6 × 24=720 - •Probability:
720 / 5040= 1/7
Why not others:
- (a) 1/168 — incorrect block position count
- (b) 1/42 — incorrect combination of factors
- (c) 1/35 — forgets internal permutations of the 3 friends (3!)
Key rule: "Sit next to each other" → treat group as a single block, then multiply: block positions × internal permutations × remaining permutations.
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