Simplify 8P3.
A.) 42
B.) 336
C.) 40,432
D.) 56
455.
15C3 represents the number of combinations of 15 items taken 3 at a time, which can be calculated using the formula:
nCr = n! / (r! * (n-r)!)
Plugging in 15 for n and 3 for r, we get:
15C3 = 15! / (3! * (15-3)!)
15! = 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
3! = 3 x 2 x 1
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
So,
15C3 = (15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) x (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
Canceling out the common factors:
15C3 = (15 x 14 x 13) / (3 x 2 x 1)
15C3 = 455
A) 47/120; 1/6
The experimental probability of rolling a 4 is the number of times 4 comes up divided by the total number of rolls:
Experimental probability = 47/120
The theoretical probability of rolling a 4 on a fair number cube is 1/6.
Therefore, the answer is (A) 47/120 for experimental probability and 1/6 for theoretical probability.
The experimental probability of winning a free gallon of milk can be calculated by dividing the number of customers who have received a star on their receipt by the total number of customers who have made a purchase.
Since 147 out of the first 156 customers did not receive a star, it means that only 9 customers received a star on their receipt.
Therefore, the experimental probability of winning a free gallon of milk is 9/156, which simplifies to 3/52.
P(red, then blue) = P(red) × P(blue) = (9/41) × (10/41) = 90/1681
Since the marble is replaced after the first pick, the probability of picking a red marble on the first pick is 9/41 (since there are 9 red marbles out of a total of 41 marbles).
The probability of picking a blue marble on the second pick is also 10/41 (since the marble is replaced and there are still 10 blue marbles remaining out of 41 total marbles).
Therefore, the probability of picking a red marble and then a blue marble is the product of the individual probabilities, which is (9/41) × (10/41) = 90/1681.
Hence, the answer is (C) 90/1681.
B) 336
8P3 means the number of permutations of 8 things taken 3 at a time.
The formula for permutations is:
nPr = n! / (n - r)!
where n is the total number of items and r is the number of items chosen at a time.
Plugging in 8 for n and 3 for r:
8P3 = 8! / (8 - 3)!
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
(8 - 3)! = 5! = 5 x 4 x 3 x 2 x 1
So,
8P3 = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (5 x 4 x 3 x 2 x 1)
Canceling out the common factors:
8P3 = 8 x 7 x 6 = 336
@bot simplify 15C3.
@bot A number cube is rolled 120 times. The number 4 comes up 47 times. What is the experimental probability of rolling a 4? what is the theoretical probability of rolling a 4?
A 47/120 ; 1/30 B 47/120 ; 1/6 C 4/47 ; 1/6 D 1/6 ; 47/120
@bot A spinner is divided into 11 equal sections numbered from 0 to 10. You spin the spinner once. what is P(not even)?
@bot Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 147 of the first 156 customers have not received a star on their receipts. What is the experimental probability of winning a free gallon of milk?
@bot A bag contains 7 green marbles, 9 red marbles, 10 orange marbles, 5 brown marbles and 10 blue marbles. You choose a marble, replace it, and choose again what is P(red, than blue)
A77/164 B19/41 C 90/1681 D 45/41