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Bell Numbers

Bell numbers are a sequence of integers that count the number of ways to partition a set of n elements into non-empty subsets.

14 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is the formula for the Bell number B(n)?

  1. B(n) = (1/e) * sum(k! * S(n, k) for k from 0 to n)
  2. B(n) = (1/e) * sum(k! * S(n, k) for k from 1 to n)
  3. B(n) = (1/e) * sum(k! * S(n, k) for k from 2 to n)
  4. B(n) = (1/e) * sum(k! * S(n, k) for k from 3 to n)
Question 2 Multiple Choice (Single Answer)

What is the Bell number for n = 3?

  1. 5
  2. 10
  3. 15
  4. 20
Question 3 Multiple Choice (Single Answer)

What is the Bell number for n = 4?

  1. 15
  2. 20
  3. 25
  4. 30
Question 4 Multiple Choice (Single Answer)

What is the Bell number for n = 5?

  1. 52
  2. 60
  3. 68
  4. 76
Question 5 Multiple Choice (Single Answer)

What is the Bell number for n = 6?

  1. 203
  2. 220
  3. 238
  4. 256
Question 6 Multiple Choice (Single Answer)

What is the Bell number for n = 7?

  1. 877
  2. 924
  3. 972
  4. 1020
Question 7 Multiple Choice (Single Answer)

What is the Bell number for n = 8?

  1. 4140
  2. 4320
  3. 4500
  4. 4680
Question 8 Multiple Choice (Single Answer)

What is the Bell number for n = 9?

  1. 21147
  2. 21900
  3. 22663
  4. 23436
Question 9 Multiple Choice (Single Answer)

What is the Bell number for n = 10?

  1. 115975
  2. 118750
  3. 121535
  4. 124320
Question 10 Multiple Choice (Single Answer)

What is the relationship between Bell numbers and Stirling numbers of the second kind?

  1. B(n) = (1/e) * sum(k! * S(n, k) for k from 0 to n)
  2. B(n) = (1/e) * sum(k! * S(n, k) for k from 1 to n)
  3. B(n) = (1/e) * sum(k! * S(n, k) for k from 2 to n)
  4. B(n) = (1/e) * sum(k! * S(n, k) for k from 3 to n)
Question 11 Multiple Choice (Single Answer)

What is the asymptotic formula for the Bell number B(n)?

  1. B(n) ~ (1/sqrt(2 * pi * n)) * (n/e)^n
  2. B(n) ~ (1/sqrt(2 * pi * n)) * ((n+1)/e)^(n+1)
  3. B(n) ~ (1/sqrt(2 * pi * n)) * ((n-1)/e)^(n-1)
  4. B(n) ~ (1/sqrt(2 * pi * n)) * ((n+2)/e)^(n+2)
Question 12 Multiple Choice (Single Answer)

What is the generating function for the Bell numbers?

  1. exp(e^x - 1)
  2. exp(e^x + 1)
  3. exp(e^x - 2)
  4. exp(e^x + 2)
Question 13 Multiple Choice (Single Answer)

What is the relationship between Bell numbers and exponential generating functions?

  1. The exponential generating function for the Bell numbers is exp(e^x - 1).
  2. The exponential generating function for the Bell numbers is exp(e^x + 1).
  3. The exponential generating function for the Bell numbers is exp(e^x - 2).
  4. The exponential generating function for the Bell numbers is exp(e^x + 2).
Question 14 Multiple Choice (Single Answer)

What is the relationship between Bell numbers and derangements?

  1. The number of derangements of n elements is equal to the Bell number B(n).
  2. The number of derangements of n elements is equal to the Bell number B(n+1).
  3. The number of derangements of n elements is equal to the Bell number B(n-1).
  4. The number of derangements of n elements is equal to the Bell number B(n+2).
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