Multiple choice

There are 7 gold rings, 5 silver rings and 10 diamond rings in a bag. In how many ways can a person pick 3 rings from the bag such that at least one of them is a diamond ring?

  1. 1280

  2. 1320

  3. 1410

  4. 1480

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total rings = 7+5+10 = 22. Total ways to pick 3 rings = 22C3 = (22*21*20)/(3*2*1) = 1540. Ways to pick 3 rings with no diamonds (only gold or silver) = 12C3 = (12*11*10)/(3*2*1) = 220. Ways with at least one diamond = 1540 - 220 = 1320.

AI explanation

The bag holds a total of 22 rings, so the total ways to pick any 3 rings is the combination of 22 taken 3 at a time, which is 1540. To find the ways to pick at least one diamond ring, subtract the ways to pick zero diamond rings from the total. The ways to pick 3 rings from the 12 non-diamond rings is the combination of 12 taken 3 at a time, which is 220. The required number of ways is 1540 minus 220, resulting in 1320.

Keep practicing — related questions