Eight prizes are to be distributed by a lottery. The 1st participant takes five tickets from a box containing 50 tickets. In how many different ways can he extract them so that exactly two tickets are winning ?

Dear student, 
As there are 8 winning number,and thus 42 non winning numbers  When the participant selects 5 tickets, exactly 2 are winning numbers and 3 are non winning numbers 
so the number of ways of having exactly 2 winning number out of 5 = 42C3×8C2, as 3 non winning tickets out of 42 can be selected in 42C3and 2 winning tickets out of 8 can be selected in 8C2.So total number of ways in which exactly 2 winning tickets can come while selecting 5 tickets out of 50 , is 42C3×8C2
Hope this clears your doubt 
With regards 

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