Could someone check my answers for these questions:
62. Powerball is played with 55 white balls, numbered 1 through 55 and 42 red balls, numbered 1 through 42. Five white balls and one red ball are drawn. In how many ways can a player select the six numbers?
Answer: 141607962
64. A shipment of 25 television sets contains three defective units. In how many ways can a vending company purchase four of these units and receive (a) all good units, (b) two good units, and (c) at least two good units.
Answer:
(a) 7315
(b) 693
(c) 12628
68. A law office interviews paralegals for 10 openings. There are 13 paralegals with two years of experience and 20 paralegals with one year of experience. How many combinations of 7 paralegals with two years of experience and three paralegals with one year of experience are possible?
Answer: 1956240
I got the same answers for all of them
good job!
To check the answers for these questions, we can use combinatorial formulas.
For question 62, the number of ways to select the six numbers is given by the combination formula: C(n, k) = n! / (k!(n-k)!)
In this case, we have 55 white balls to choose from (n = 55) and need to select 5 (k = 5), and 42 red balls to choose from (n = 42) and need to select 1 (k = 1).
So, the number of ways is: C(55, 5) * C(42, 1) = 2,883,060 * 42 = 121,621,200
However, the given answer is different, so it seems to be incorrect.
For question 64, we need to consider different cases:
(a) To choose all good units, we can select 4 from the 22 good units out of 25 total units. So, the number of ways is C(22, 4) = 7,315.
(b) To choose two good units, we can select 2 from the 22 good units and 2 from the 3 defective units. So, the number of ways is C(22, 2) * C(3, 2) = 253 * 3 = 759.
(c) To choose at least two good units, we need to calculate the number of ways to choose exactly two good units or all good units.
- The number of ways to choose exactly two good units: C(22, 2) * C(3, 2) = 253 * 3 = 759 (same as part b)
- The number of ways to choose all good units: C(22, 4) = 7,315 (same as part a)
Adding these two cases, we get: 759 + 7,315 = 8,074.
Therefore, the answers are:
(a) 7,315
(b) 759
(c) 8,074
For question 68, we need to calculate the combinations of 7 paralegals with two years of experience and 3 paralegals with one year of experience.
The number of ways is: C(13, 7) * C(20, 3) = 1716 * 1140 = 1,956,240
The given answer is correct: 1,956,240.
Please recheck your answer for question 62 as there seems to be an error.