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Stats I · Permutations & combinations

BSMA1002 · 19 questions · 50 marks · 7 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1002 · Statistics for Data Science I

Permutations & combinations

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

End Term · 31 Aug 2025 (FN)End Term

Q1MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D

End Term · 31 Aug 2025 (AN)End Term

Q2MCQ2 Marks·Choose one option
Key ↓
Find the number of rearrangements of the letters in the word COMMITTEE.
1. A
2. B
3. C
4. D

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Q3MCQ3 Marks·Choose one option
Key ↓
How many numbers greater than 10,000 can be formed using the digits 0, 2, 5, 4, 6, 8 without repetition?
1. A600
2. B120
3. C240
4. D1200
Q4NAT2 Marks·Write the number
Key ↓
A company has 15 offices and wants to set up two-way communication between every pair of offices. However, the 3 smallest offices will not have direct communication with one another, though each of them can still connect directly with the remaining offices. How many communication channels are needed in total?
Your answer:
Q5NAT3 Marks·Write the number
Key ↓
A group of 4 teachers and 4 students is to be seated around a circular table for a discussion. They decide that all students must sit together. Find the number of ways they can be seated around the table such that all students are sitting together.
Your answer:
Q6NAT3 Marks·Write the number
Key ↓
A basket contains 5 red balls and 4 green balls. If 3 balls are to be selected at random without replacement, in how many ways can the balls be selected such that at least one green ball is included?
Your answer:
Q7NAT3 Marks·Write the number
Key ↓
How many 5-digit numbers can be formed using the digits 0, 2, 3, 4, and 7 where digits may be repeated such that the number is divisible by 2 ?
Your answer:
Q8NAT3 Marks·Write the number
Asked 3 times Key ↓
In how many different ways can the letters of the word ‘ARTICLE’ be arranged such that all the vowels always come together?
Your answer:
Q9NAT3 Marks·Write the number
Key ↓
A committee of 3 people is to be formed from a group of n people. The number of possible committees in which two particular people A and B are both included together is 7. Find the number of ways in which committee can be formed.
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Q10MCQ3 Marks·Choose one option
Key ↓
1. A318240
2. B78000
3. C18720
4. D39000
Q11MCQ3 Marks·Choose one option
Asked 2 times Key ↓
A group of 7 people (A, B, C, D, E, F, G) is to be seated in a row for a photograph. Find the number of possible arrangements such that D and E cannot sit next to each other.
1. A3600
2. B4320
3. C5040
4. D720

End Term · 13 Apr 2025 (AN)End Term

Q12MSQ2 Marks·Choose all correct options
Key ↓
Consider the following statements related to permutation and combination. Which of the following is/are true?
1. A
2. B
3. C
4. D
Q13NAT3 Marks·Write the number
Asked 2 times Key ↓
A group of 7 people (A, B, C, D, E, F, G) is to be seated in a row for a photograph. The following conditions must be satisfied: • A and B must always sit next to each other. • D and E cannot sit next to each other. What is the total number of valid arrangements under these conditions?
Your answer:

End Term · 22 Dec 2024 (FN)End Term

Read the passage below, then answer Q14–Q15
A university needs to form a research team of 4 students out of total 8 students.
Based on the above data answer the given subquestions.
Q14NAT2 Marks·Write the number
Asked 4 times Key ↓
In how many ways can the team be formed if two particular students must be included?
Your answer:
Q15NAT2 Marks·Write the number
Asked 4 times Key ↓
In how many ways can the team be formed if two particular students must not be included?
Your answer:
Q16NAT3 Marks·Write the number
Asked 3 times Key ↓
In how many different ways can the letters of the word “LEADING” be arranged such that the vowels always come together?
Your answer:

End Term · 22 Dec 2024 (AN)End Term

Read the passage below, then answer Q17–Q18
A university needs to form a research team of 4 students out of total 9 students.
Based on the above data answer the given subquestions.
Q17NAT2 Marks·Write the number
Asked 4 times Key ↓
In how many ways can the team be formed if two particular students must be included?
Your answer:
Q18NAT2 Marks·Write the number
Asked 4 times Key ↓
In how many ways can the team be formed if two particular students must not be included?
Your answer:
Q19NAT3 Marks·Write the number
Asked 3 times Key ↓
In how many different ways can the letters of the word “READING” be arranged such that the vowels always come together?
Your answer:

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q1A, B, C

Q2D

Q3D

Q4102

Q5576

Q674

Q71500

Q8720

Q984

Q10B

Q11A

Q12A, D

Q13960

Q1415

Q1515

Q16720

Q1721

Q1835

Q19720

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.