The way I thought about this problem is:

X = 1 if young

X = 0 if old

Y = 1 if male

Y = 0 if female

Z = 1 if married

Z = 0 if single

So using the given numbers:

P(X) = 3000/10000 and P(X') = 7000/10000

P(Y) = 4600/10000 and P(Y') = 5400/10000

P(Z) = 7000/10000 and P(Z') = 3000/10000

P(XY) = P(Young Male) = 1320/10000

P(YZ) = P(Married Male) = 3010/10000

P(XZ) = P(Young Married) = 1400/10000

P(XYZ) = P(Young Male Married) = 600/10000

To get P(Young Female Single), use the law of total probability until you get all of the probabilities you need to calculate P(XY'Z'). For example:

P(XY) = P(XYZ) + P(XYZ')

P(XYZ') = P(XY) - P(XYZ) = 700/10000 = P(Young Male Single)

Etc.