Minimalist IAS
Sign up
English हिंदी
CSAT

CSAT · 43 questions

Counting, permutations & probability

Every UPSC CSAT question on this topic, 2016–2026, newest first. Tap an option to check yourself; the answer and explanation open below it.

Counting, permutations & probability questions per year: 2016: 4, 2017: 3, 2018: 4, 2019: 4, 2020: 2, 2021: 3, 2022: 8, 2023: 11, 2024: 1, 2025: 0, 2026: 3 Asked in 10 of 11 years · most in 2023 (11)
Timed · 30 minutes a set Practise Counting, permutations & probability as timed tests 2 sets of about 20 questions with UPSC's CSAT marking. Start practising

UPSC syllabus: “Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level), Data interpretation (charts, graphs, tables, data sufficiency etc. — Class X level);” Sub-topics in the detailed syllabus →

CSAT 2020 · Q60

Medium

मूल्यवर्गों ₹ 50, ₹ 100, ₹ 200, ₹ 500 और ₹ 2,000 के साथ, एक समय में कम-से-कम तीन मूल्यवर्गों को लेते हुए, कितनी विभिन्न धनराशियाँ बनाई जा सकती हैं?

Read this question in English

How many different sums can be formed with the denominations ₹ 50, ₹ 100, ₹ 200, ₹ 500 and ₹ 2,000 taking at least three denominations at a time?

(a) 16 · (b) 15 · (c) 14 · (d) 10

उत्तर और व्याख्या · explanation in English

Answer: (a) 16

Choosing 3, 4 or all 5 of the five denominations gives 10 + 5 + 1 = 16 selections. Each denomination is more than the sum of all the smaller ones, so no two selections can give the same amount — all 16 sums are different.

  1. Ways to choose 3, 4 or 5 of 5 denominations: ⁵C₃ + ⁵C₄ + ⁵C₅ = 10 + 5 + 1 = 16.
  2. 100 > 50, 200 > 50 + 100, 500 > 50 + 100 + 200 and 2,000 > 850, so different selections always give different totals.
  3. Number of different sums = 16.
  4. Check: the 16 sums run from ₹ 350 (50 + 100 + 200) to ₹ 2,850 (all five) with no repeats.

Remember · Count selections with nCr, then check whether two selections can give the same total before answering.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2020 · Q67

Easy

शब्द ‘DELHI’ के सभी अक्षरों का प्रयोग करते हुए कितने विभिन्न 5-अक्षरी शब्द (जिनका कोई अर्थ हो या न हो) बनाए जा सकते हैं, जबकि प्रत्येक शब्द D के साथ शुरू होता है और I के साथ समाप्त होता है?

Read this question in English

How many different 5-letter words (with or without meaning) can be constructed using all the letters of the word ‘DELHI’ so that each word has to start with D and end with I?

(a) 24 · (b) 18 · (c) 12 · (d) 6

उत्तर और व्याख्या · explanation in English

Answer: (d) 6

With D fixed first and I fixed last, only E, L and H are left to arrange in the three middle places. Three distinct letters can be arranged in 3! = 6 ways.

  1. Positions 1 and 5 are fixed: D _ _ _ I.
  2. E, L and H fill the three middle places in 3! = 3 × 2 × 1 = 6 ways.
  3. Check: DELHI, DEHLI, DLEHI, DLHEI, DHELI, DHLEI — six words.

Remember · Fix the letters whose places are given, then arrange only the remaining ones: n distinct letters give n! orders.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

The Syllabus X-Ray of this topic

1 of its 3 sub-topics is High

0 Core · 1 High · 2 Steady · 0 Rare

  • HighCounting figures & cases · 37 questions

The X-Ray ranks all 928 sub-topics of the UPSC syllabus by what UPSC has asked since 2016. The 6 CSAT Core sub-topics are behind 50% of CSAT questions.

See the whole X-Ray →

Other CSAT skills