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In how many ways can 5 different objects be selected from 10 objects?

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Question: In how many ways can 5 different objects be selected from 10 objects?

Options:

  1. 252
  2. 120
  3. 10
  4. 100

Correct Answer: 252

Solution: 

The number of ways to select 5 objects from 10 is 10C5 = 10! / (5! * 5!) = 252.

In how many ways can 5 different objects be selected from 10 objects?

Practice Questions

Q1
In how many ways can 5 different objects be selected from 10 objects?
  1. 252
  2. 120
  3. 10
  4. 100

Questions & Step-by-Step Solutions

In how many ways can 5 different objects be selected from 10 objects?
Correct Answer: 252
  • Step 1: Understand that we want to choose 5 different objects from a total of 10 objects.
  • Step 2: Recognize that this is a combination problem, where the order of selection does not matter.
  • Step 3: Use the combination formula, which is written as nCr, where n is the total number of objects and r is the number of objects to choose. Here, n = 10 and r = 5.
  • Step 4: The formula for combinations is nCr = n! / (r! * (n - r)!).
  • Step 5: Plug in the values: 10C5 = 10! / (5! * (10 - 5)!) = 10! / (5! * 5!).
  • Step 6: Calculate 10! (10 factorial), which is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.
  • Step 7: Calculate 5! (5 factorial), which is 5 x 4 x 3 x 2 x 1.
  • Step 8: Substitute the factorial values into the formula: 10C5 = (10 x 9 x 8 x 7 x 6) / (5 x 4 x 3 x 2 x 1).
  • Step 9: Simplify the calculation: 10C5 = 252.
  • Step 10: Conclude that there are 252 different ways to select 5 objects from 10.
  • Combinatorics – The study of counting, arrangements, and combinations of objects.
  • Binomial Coefficient – The formula used to determine the number of ways to choose a subset of items from a larger set, denoted as nCr.
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