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# Probability

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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.

Dec 7, 2021

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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.

Dec 8, 2021