IPMAT Indore 2025 · Quantitative Ability · Question 10
IPMAT Indore 2025 previous year question on Permutation and Combination, with the answer and a step-by-step solution.
Eight teams participate in a tournament where each team plays against every other team exactly once. In a particular year, one team got suspended after playing 3 matches, due to a disciplinary issue. The organisers decided to proceed, nonetheless, with the remaining matches. The total number of matches that were played in the tournament that year is
Answer & solution
Answer: 24
Step 1 — the full schedule. Every pair of teams meets once, so the number of matches is the number of ways of choosing 2 teams out of 8:
\left( \genfrac{}{}{0pt}{}{8}{2}\right)=\frac{8\times 7}{2}=28
Step 2 — what the suspension costs. The suspended team was supposed to play 8-1=7 matches. It actually played 3, so
7-3=4\text{matches were never played.}
Every other match in the schedule involves two surviving teams, so all of those still went ahead.
Step 3 — subtract.
28-4=24
Answer: 24
More Permutation and Combination questions
- Q1In a chess tournament, there are four groups, each containing an equal number of players. Each player plays against…IPMAT Indore 2023 · Quantitative Ability · Permutation and Combination
- Q12The total number of positive integer solutions of 21≤ a+b+c≤ 25 is _____IPMAT Indore 2023 · Quantitative Ability · Permutation and Combination
- Q23Consider an 8 × 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the…IPMAT Indore 2023 · Quantitative Ability · Permutation and Combination
- Q25A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing…IPMAT Indore 2023 · Quantitative Ability · Permutation and Combination
- Q39The number of integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where…IPMAT Indore 2025 · Quantitative Ability · Permutation and Combination
- Q32Let n be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that…IPMAT Indore 2024 · Quantitative Ability · Permutation and Combination
All Permutation and Combination PYQs →
Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.