p1= (4/7) * (5/9) * (4/8)

p2 = (4/7) * (4/9) * (4/8)

p3 = (3/7) * (5/9) * (4/8)

p_total=p1+p2+p3

numerator = 80+64+60 denominator=504

def gcd(a,b): while b !=0: a,b =b, a%b return a

g=gcd(numerator,denominator)

numerator //=g denominator //=g

print(f"{numerator}/{denominator}")

check out the link for solution in python with explanation, https://youtu.be/S8OPaYOUC6s?si=-6XHBgwJUrl_BqL7

from fractions import Fraction temp_X=7 temp_Y=9 temp_Z=8 RED_X,RED_Y,RED_Z=4,5,4 BLACK_X,BLACK_Y,BLACK_Z=3,4,4 P_R_X = RED_X/temp_X P_B_X=BLACK_X/temp_X P_R_Y=RED_Y/temp_Y P_B_Y=BLACK_Y/temp_Y P_B_Z=BLACK_Z/temp_Z P_R_Z=RED_Z/temp_Z P1 = P_R_X * P_R_Y * P_B_Z P2 = P_R_X * P_B_Y * P_R_Z P3 = P_B_X * P_R_Y * P_R_Z

temp = P1+P2+P3 print(Fraction(temp).limit_denominator(), temp)

java

public class Solution{

public static void main(String[] args) {
    char[] X = {'r','r','r','r','b','b','b'};
    char[] Y = {'r','r','r','r','r','b','b','b','b'};
    char[] Z = {'r','r','r','r','b','b','b','b'};
    int denom = X.length*Y.length*Z.length;

    int reds=0;
    int count =0;

    for(char x : X){
        if(x=='r') reds++;
        for(char y : Y){
            if(y=='r') reds++;
            for(char z : Z){
                if(z=='r') reds++;
                if(reds==2) {
                    count++;
                }
                if(z=='r') reds--;
            }
            if(y=='r') reds--;
        }
        reds=0;
    }

    for (int i = 2; i < Math.sqrt(denom); i++) {
        if (denom % i == 0 && count % i == 0) {
            denom = denom / i;
            count = count / i;
            i--;

        }
    }

    System.out.println(count +"/"+denom);
}

}