+0  
 
0
55
1
avatar

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
 #1
avatar+115901 
+1

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

11 Online Users

avatar
avatar