Since 5 winning numbers are draw and there are exactly 2 winning numbers, the other 3 numbers chosen have to be incorrect.
The 2 numbers picked right, there are 5C2=10 different possibilities.
The other 3 numbers are just picked from the rest of the 32 numbers. Getting there are 32C3=4960 different possibilities.
For each set of 2 correct winning numbers, you could have the 4960 different losing numbers to match up to make a unique set. This meant that there are 4690*10=46900 different total possibilities.
Now the total different outcomes of how you can choose the numbers are 37C5=435897 outcomes.
Now the way to find probabilities is want/total
The want is 46900 and the total is 435897
Doing the division you get the number rounded to the nearest thousandths as 0.107 or in percent form as
10.759% chance of picking exactly 2 winning numbers.
This seems like a competition problem of some sort therefore I assume that you already know what combinations in form nCk and permutation in form nPk means.
(2x^2 +6x) + (5x +15)
GCF for the 1st group is 2x and the 2nd is 5
2x(x +3) + 5(x +3)
(2x +5) (x+3)
Let n = the unknown number
"The product of a number and 4" = 4 * n = 4n
"increased by 16" = + 16
Set it all equal to - 2.
4n + 16 = - 2
Subtract 16 from both sides to get constants on one side and variables on the other.
4n = - 2 - 16
Combine like terms:
4n = - 18
Divide both sides by 4 to isolate variable n.
n = - 18 / 4
= - 4 and 2/4 = - 4 and 1/2
Answer:
4 raised to 4 is 256
Step-by-step explanation:
