My Learning Cart
?
Categories
Account

A charity event has 5 awards to give out among 10 nominees. If each nominee can

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: A charity event has 5 awards to give out among 10 nominees. If each nominee can win only one award, how many different combinations of award winners are possible?

Options:

  1. 252
  2. 120
  3. 210
  4. 300

Correct Answer: 252

Solution: 

The number of combinations is calculated using the formula for combinations: C(10, 5) = 10! / (5!(10-5)!) = 252.

A charity event has 5 awards to give out among 10 nominees. If each nominee can

Practice Questions

Q1
A charity event has 5 awards to give out among 10 nominees. If each nominee can win only one award, how many different combinations of award winners are possible?
  1. 252
  2. 120
  3. 210
  4. 300

Questions & Step-by-Step Solutions

A charity event has 5 awards to give out among 10 nominees. If each nominee can win only one award, how many different combinations of award winners are possible?
  • Step 1: Understand that we have 10 nominees and we want to choose 5 of them to win awards.
  • Step 2: Recognize that the order in which we choose the nominees does not matter, so we will use combinations instead of permutations.
  • Step 3: Use the combinations formula, which is C(n, r) = n! / (r!(n-r)!), where n is the total number of items (nominees) and r is the number of items to choose (awards).
  • Step 4: In this case, n = 10 (nominees) and r = 5 (awards). So we will calculate C(10, 5).
  • Step 5: Plug the values into the formula: C(10, 5) = 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! (we can stop at 5! because it will cancel out).
  • Step 7: Now we have: C(10, 5) = (10 x 9 x 8 x 7 x 6) / (5 x 4 x 3 x 2 x 1).
  • Step 8: Calculate the numerator: 10 x 9 x 8 x 7 x 6 = 30240.
  • Step 9: Calculate the denominator: 5 x 4 x 3 x 2 x 1 = 120.
  • Step 10: Divide the numerator by the denominator: 30240 / 120 = 252.
  • Step 11: Conclude that there are 252 different combinations of award winners possible.
  • Combinations – The concept of combinations involves selecting items from a larger set where the order of selection does not matter.
  • Factorials – Factorials are used in the calculation of combinations, representing the product of all positive integers up to a given number.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks