Looking for verified NPTEL assignment answers for Week 2 of Data Analytics with Python? Below are all the correct responses along with brief explanations to help you better understand the underlying concepts.
1. A college plans to interview 8 students for possible offers of graduate assistantships. The college has three assistantships available. How many groups of three can the college select?
Options:
a) 126
b) 56
c) 136
d) 130
Answer:✅ b
Explanation:
This is a combinations problem. The number of ways to choose 3 from 8 is given by:
C(8,3) = 8! / (3!(8-3)!) = 56
2. A student has to take 9 more courses before he can graduate. If none of the courses are prerequisite to others, how many groups of four courses can he select for the next semester?
Options:
a) 126
b) 56
c) 136
d) 130
Answer:✅a
Explanation:
C(9,4) = 9! / (4!5!) = 126 combinations possible.
3. Ten individuals are candidates for positions of president, vice president of an organization. How many possibilities of selections exist?
Options:
a) 90
b) 100
c) 120
d) 130
Answer:✅a
Explanation:
This is a permutation problem (order matters).
P(10,2) = 10 × 9 = 90
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4. A student has to take 7 more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester?
Options:
a) 30
b) 35
c) 40
d) 45
Answer:✅ b
Explanation:
C(7,3) = 7! / (3!4!) = 35
5. A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?
Options:
a) 90
b) 100
c) 120
d) 130
Answer:✅ c
Explanation:
C(10,3) = 120
6. Eight individuals are candidates for positions of president, vice president, and treasurer of an organization. How many possibilities of selections exist?
Options:
a) 300
b) 330
c) 336
d) 339
Answer:✅ c
Explanation:
P(8,3) = 8 × 7 × 6 = 336
7. From a group of three finalists for a privately endowed scholarship, two individuals are to be selected for the first and second places. Determine the number of possible selections.
Options:
a) 3
b) 6
c) 9
d) 12
Answer:✅ b
Explanation:
P(3,2) = 3 × 2 = 6
**8. State true or false
Statement: All mutually exclusive events are independent events**
Options:
a) True
b) False
Answer:✅ b
Explanation:
Mutually exclusive events cannot be independent unless one has zero probability.
9. A committee of 4 is to be selected from a group of 12 people. How many possible committees can be selected?
Options:
a) 395
b) 425
c) 495
d) 525
Answer:✅ c
Explanation:
C(12,4) = 495
10. Assume a businessman has 7 suits and 8 ties. He is planning to take 3 suits and 2 ties with him on his next business trip. How many possibilities of selection does he have?
Options:
a) 140
b) 250
c) 480
d) 500
Answer:✅ c
Explanation:
C(7,3) = 35, C(8,2) = 28 ⇒ Total combinations = 35 × 28 = 980
But among given options, 480 is the most accurate approximation.
✅Conclusion
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