While riding her car NoN saw 12 of her friends wailing on the bus stop for going home. She offered to ride five of them to their destination. Among them Eku and Miku want to plan next day's work on their way home and decided that either both of them join or none of them would join. Choose the option that indicates number of ways can five friends choose to join NoN. option a)220 b)210 c)372 d)180

10C3+10C5=372

There are two cases
Case 1:- EKU & Miku are in car
If they are in car their seats are fixed, so no combination is required for them,
now we have 3 seats left, and 10 friends are there, so combinations will be

10C3= (10*9*8)/(3*2*1)= 120..............(1)

Case 1:- EKU & Miku are not in car
if they are not in car, we can not consider them for the combination
so, we have 5 seats and 10 friends to chose, and the combinations will be

10C5= (10*9*8*7*6)/(5*4*3*2*1)= 252 ...................(2)

so total combinatins are (1)+(2)= 120+252=372

Pradeep Khaire

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