In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 6 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel? Choose the correct choice from the following choices
A) 27/343
B) 3/7
C) 27/125
D) 776/965
E) 9/125
Let us take 7*5= 
<gadget id="calculator">7*5</gadget>
<output>35</output>
35 as the total number of customers. So  7*3= 
<gadget id="calculator"> 7*3</gadget>
<output>21</output>
21 customers bought a bagel and 5*5= 
<gadget id="calculator">5*5</gadget>
<output>25</output>
25 customers bought a coffee.   chances that at least 1 customer bought a coffee and a bagel= 1 - chances that no customer bought a coffee and a bagel   chances that no customer bought a coffee and a bagel= 24/35*23/34*22/33*21/32*20/31*19/30=189/965   chances that at least 1 customer bought a coffee and a bagel= 1 -189/965 = 776/965   Answer 776/965.
<result>D</result>
In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 6 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?