ITPEC FE Morning October 2023 Question 3
Source exam: ITPEC FE Morning October 2023Topic: Basic Theory & Math
ITPEC FE Morning October 2023 — Question 3 of 80
Probability of adjacent empty spaces — count favorable block positions vs. total combinations.
Given 10 spaces in a row with 3 empty:
- •Total ways to choose 3 empty from 10:
C(10,3) = 120 - •Favorable: block of 3 adjacent can start at positions 1–8 →
8ways - •Probability:
8 / 120 = 1/15
Why not others:
- (a) 1/90 — incorrect combination count
- (b) 1/72 — incorrect combination count
- (d) 1/12 — overcounts block positions
Key rule: For "all K items adjacent in N slots," favorable outcomes = N − K + 1, total = C(N, K).
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