Coin Die Set

Coin Die Set
Are my answers to these probability problems correct?

If they’re wrong, can you give me the correct answer?

4. In an exam, a student is required to answer exactly 8 questions from 10 multiple-choice questions and work exactly 2 problems out of 5 word problems. In how many ways can she make her selections? 450

8. What is the probability that in tossing a fair die five times, you will get a number less than 4 at least once? 1/2

19. You own 30 compact disks but can only load six in your car at a time. How many different sets of six disks can you load? 593,775

20. How many outcomes are possible of tossing one coin and then rolling one die? 12

24. What is the probability of selecting all men for a 4-person panel from a pool of 10 men and 10 women? 14/323

25. What are the chances of obtaining a sum larger than 16 in three throws of a fair die? 1/18

4 and 20 are correct.

I got the same answers you did for 19 and 24.

8. The probability that in tossing a fair die once, you will get a number less than 4 is 1/2. But the problem asks for the probability of doing so at least once in five tries. That is
1 – the probability of not doing so at all
and the probability of not doing so at all is (1/2)^5 because we have five independent tries. So the correct answer is
1 – (1/2)^5 = 1 – 1^5/2^5 = 1 – 1/32 = 31/32.

25. There is only one way to roll 18 (all sixes), and there are only three ways to roll 17 (two sixes and a five, with the five first, second, or third). That’s
4/6^3 = 4/216 = 1/54.
You lost a factor of three in the denominator somewhere.

Super Mario Galaxy – Buoy Base Galaxy, All 50 Coins