Valentine Vinculum!
A class has an equal number of boys and girls. One third of the boys in the class
shook hands with each girl and one fourth of the girls shook hands with each boy.
Each of the remaining boys brought a rose for one or the other of the remaining girls.
In the end, three of the remaining girls didn't get a rose.
How many handshakes were done?
Details : No two persons shook hands twice.
The answer is 648.
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consider no. of boys = x = no. of girls so, as in question x/3 boys shook hands with each one of the girls(x) and x/4 girls shook hands with each boy (x) remaining no. of boys =2x/3 remaining no. of girls = 3x/4 but , 3x/4 - 2x/3 = 3 because 3 girls are left without rose in the end therefore , x = 36 to find the total no. of handshakes we find no. of handshakes between x/3 boys and x girls and between 2x/3 boys and x/4 girls i.e. 12C1 * 36C1 + 9C1* 24C1