Party all night
Microsoft has called a party for for its some special employees. So in the party there appears 5 Indian couples and 5 American couples. They meet and handshake to each other. Now if no Indian wife shakes hand with any male and no wife does not shake hand with her husband then how many handshakes took place in the party?
The answer is 135.
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1 solution
At first let us group the persons present into Indian males, Indian females , american males and american females. Now all groups complete handshakes inside groups first. 5 people can have 5C2 =10 handshakes. Now there occurs total of 40 handshakes. Now Indian women comes one by one and one woman handshakes with 5 american women. Hence 5×5=25 handshakes takes place. Now we have this pattern for three categories of handshakes. These are indo American male-male, indoamerican female-female and indo american male- female.thus in this category there occurs 25×3=75 handshakes. Now Indian couples are done and they leave the place. Now one by one American women come and handshake with the other 4 males except her husband. Thus occurs 5×4=20 handshakes. So there are at total 40+75+20=135 handshakes. A whole lot of handshakes:)