Mike draws six cards from a standard 52-card deck. What is the probability that he draws a card from at least three of the four suits? Express your answer as a simplified fraction.
+118608 Mike draws six cards from a standard 52-card deck. What is the probability that he draws a card from at least three of the four suits? Express your answer as a simplified fraction.
52C6 = 20358520 ways to choose 6 cards from a deck
lets see what doesn't work
all 6 the same 4*13C6 = 6864
5 the same the other different 4*13C5*39 = 200772
4 the same and same and 2 the same 4C2*2*13C4*13C2 = 669240
3 the same, 3 the same 4C2*13C3*13C3 = 490776
6864+200772+669240+490776 = 1367652
20358520-1367652 = 18990868
18990868/20358520 = 0.9328216392940155
factor(18990868) = (2^2*13^3)*2161
factor(20358520) = ((((2^3*5)*7^2)*13)*17)*47
\(\frac{18990868\div 4}{20358520\div 4}=\frac{4747717}{5089630}\)
And I do not think that can be further simplified.
If you are given an answer that is different (with some working or explanation) then please share it with us.
