# 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 ?

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 = ${42}_{{C}_{3}}\times {8}_{{C}_{2}},as3nonwinningticketsoutof42canbeselectedin{42}_{{C}_{3}}\phantom{\rule{0ex}{0ex}}and2winningticketsoutof8canbeselectedin{8}_{{C}_{2}}.\phantom{\rule{0ex}{0ex}}Sototalnumberofwaysinwhichexactly2winningticketscancomewhileselecting5tickets\phantom{\rule{0ex}{0ex}}outof50,is{42}_{{C}_{3}}\times {8}_{{C}_{2}}$

Hope this clears your doubt

With regards

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