Answer:
1,404,000 unique passwords are possible.
Step-by-step explanation:
The order in which the letters and the digits are is important(AB is a different password than BA), which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
In this question:
2 digits from a set of 10(there are 10 possible digits, 0-9).
3 characters from a set of 26. So
1,404,000 unique passwords are possible.
400 - 2 x Age = 244
-2*Age = -156
Age = 78 years
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.
D)
6 5/8
or 6.625
Basically
1/8*3 =0.375
1/4 * 3 =0.75
1/2*5 =2.5
and 3/4*4=3
So then,
0.375+0.75+2.5+3=6.625 or 6 5/8 in fraction!
