Answer:
, 60.494%
Step-by-step explanation:
I am going to try to tackle this. I might miss a step as I am currently taking discrete mathematics.
We want to find all the possibilities with 1y, 2ys, 3ys, and 4ys, out of all total possibilities.
_ _ _ _ _ _ _ _ _
For the letters, in each spot, we have 3 choices. For the numbers, we have 10 choices in each spot
so
3*3*3*3 * 10*10*10*10*10
= 81*100000
= 8100000
The number of Y's will never affect the number of permutations of the numbers.
So:
For 1 y, we have
Y _ _ _ * 10*10*10*10*10
But we also have
_ Y _ _
_ _ Y _
and
_ _ _ Y
So we can multiply the number we get in one calculation by 4
4 *
Y _ _ _ * 10*10*10*10*10
2*2*2 * 10*10*10*10*10
= 800000 * 4 = 3200000
For 2 y's, we have
YY _ _
_ YY _
__ YY
3*
YY 2*2 * 10^5
4 * 100000
400000 * 3 = 1200000
For 3 y's, we have
YYY _
_ YYY
2 *
YYY 2 * 10^5
200000 * 2
= 400000
For 4 y's, we have
YYYY * 10^5
100000
Now we can add them all up and divide it by our original number 8100000