In a 9th grade class consisting of 17 girls and 13 boys, each student shakes han

Question

In a 9th grade class consisting of 17 girls and 13 boys, each student shakes hands with each classmate exactly once. What percentage of these handshakes takes place with two students of the same gender

In a 9th grade class consisting of 17 girls and 13 boys, each student shakes hands with each classmate exactly once. What percentage of these handshakes takes place with two students of the same gender

In a 9th grade class consisting of 17 girls and 13 boys, each student shakes hands with each classmate exactly once. What percentage of these handshakes takes place with two students of the same gender
In a 9th grade class consisting of 17 girls and 13 boys, each student shakes hands with each classmate exactly once. What percentage of these handshakes takes place with two students of the same gender

Explanation / Answer

Total number of students in a class = 30

So total number of handshakes = 1+2+3+4+......+29 = 29*30/2 = 435

Total number of girls = 17

So total number of handshakes between girls = 1+2+3+4+......+16 = 16*17/2 = 136

Total number of boys = 13

So total number of handshakes between boys = 1+2+3+4+......+12 = 12*13/2 = 78

Total number of handshakes between two students of same gender = 136+78 = 214

Percentage of the handshakes between two students of the same gender to the total number of handshakes = (214/435) * 100 = 49.1954%

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