Use the permutation formula to determine the number of outcomes : 7P4
840
35
28••
2,520
Use the permutation formula to determine the number of outcomes: 10^P2
20
90
100••
720
Disagree
7P4 = 7*6*5*4 = ?
10P2 = 10*9 = ?
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Now, let's solve the problems!
For the first one, we have 7P4. Using the permutation formula, we calculate it as 7! / (7-4)! = 7! / 3! = 7 * 6 * 5 * 4 = 840. So the answer is 840.
Now, for the second one, we have 10^P2. Using the permutation formula, we calculate it as 10! / (10-2)! = 10! / 8! = 10 * 9 = 90. So the answer is 90.
I hope that puts a smile on your face! Let me know if there's anything else I can help with.
To find the number of outcomes using the permutation formula, you can use the formula P(n, r) = n! / (n - r)!, where "n" represents the total number of items and "r" represents the number of items selected.
First, let's calculate the number of outcomes for 7P4:
P(7, 4) = 7! / (7 - 4)!
= 7! / 3!
= (7 × 6 × 5 × 4 × 3 × 2 × 1) / (3 × 2 × 1)
= 840
Therefore, there are 840 different outcomes.
Next, let's calculate the number of outcomes for 10P2:
P(10, 2) = 10! / (10 - 2)!
= 10! / 8!
= (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)
= 10 × 9
= 90
Therefore, there are 90 different outcomes.
To determine the number of outcomes using the permutation formula, you can use the formula:
nPk = n! / (n - k)!
where n is the total number of items and k is the number of items selected.
For the first question, you need to calculate 7P4. Substituting the values into the formula:
7P4 = 7! / (7 - 4)!
Calculating the factorial values:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
= 5040
(7 - 4)! = 3!
Calculating 3!:
3! = 3 x 2 x 1
= 6
Now, substituting the values back into the formula:
7P4 = 5040 / 6
= 840
Therefore, the number of outcomes for 7P4 is 840.
For the second question, you need to calculate 10^P2. Substituting the values into the formula:
10^P2 = 10! / (10 - 2)!
Calculating the factorial values:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 3,628,800
(10 - 2)! = 8!
Calculating 8!:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 40,320
Now, substituting the values back into the formula:
10^P2 = 3,628,800 / 40,320
= 90
Therefore, the number of outcomes for 10^P2 is 90.