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I have a doubt on this question. It says that each business executive shakes the hand of every other B. Executive. From this statement, I understand that each B. Executvies shakes hands with 4 of the other business executives. Can someone explain me why we are considering that all B. Executives shake hands with each other?
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tatianamontllonch
I have a doubt on this question. It says that each business executive shakes the hand of every other B. Executive. From this statement, I understand that each B. Executvies shakes hands with 4 of the other business executives. Can someone explain me why we are considering that all B. Executives shake hands with each other?

The statement "each business executive shakes the hand of every other business executive" means that each executive shakes hands with the other 9 executives, not just 4. They shake hands with all other executives present, excluding themselves.
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Another way to approach this is: When a group shakes hands within itself, then the number of handshakes are counted twice as when A shakes hands with B, B is also shaking hands with A. Hence, easy way is to divide the total number of handshakes by 2 within a group to avoid double counting and count total number of handshakes between different groups by simple multiplication. Here, it will be [(10*9)/2] + 10*7 = (90/2) + 70 = 115.
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Bunuel
10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?

A. 144
B. 131
C. 115
D. 90
E. 45

Step 1: Execs shake hands everyone
Ways to choose * Choices = 10 execs * 16 (they don't shake their own hand) = 160

Step 2: chairmen shake hands with execs
Ways * Choices = 7 * 10 = 70

160+70 = 230, now we divide by 2 to get rid of the extras (there is no difference between person A shaking hands with B or person B shaking hands with A) 230/2 = 115.
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Bunuel how did you get 10C2 for the number of handshakes between business executives? I am struggling to understand how you got the 2 from 10C2. I appreciate the help.
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shenwenlim
Bunuel how did you get 10C2 for the number of handshakes between business executives? I am struggling to understand how you got the 2 from 10C2. I appreciate the help.

2 people engage in a handshake. So, the number of handshakes between 10 people is the number of pairs possible out of 10 people, hence 10C2.
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Hi,
I have a question that: why do 10 business executive shaking hands with 7 chairmen turning into 10 x 7 = 70, meanwhile 10 business executive we cannot do the same thing?
For example, we have 10 business exe, we divide them into 2 groups: 5 5. Thus, 5 x 5 = 25 can be the number of shaking-hand turns between business executives. Can you please explain this one?
Thank you in advance,
Best regards
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HenryHai
At a conference, there are 10 business executives and 7 chairmen. If each business executive shakes hands with every other executive and each chairman exactly once, and each chairman shakes hands only with the business executives (but not with other chairmen), how many handshakes take place?

A. 144
B. 131
C. 115
D. 90
E. 45

Hi,
I have a question that: why do 10 business executive shaking hands with 7 chairmen turning into 10 x 7 = 70, meanwhile 10 business executive we cannot do the same thing?
For example, we have 10 business exe, we divide them into 2 groups: 5 5. Thus, 5 x 5 = 25 can be the number of shaking-hand turns between business executives. Can you please explain this one?
Thank you in advance,
Best regards

Because dividing the 10 business executives into two groups of 5 omits the handshakes within each group. In each group of 5, the handshakes amount to 5C2 = 10. Adding these to the 25 handshakes between the two groups gives 25 + 10 + 10 = 45. This matches the result of the standard calculation, 10C2 = 45.
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I have a doubt, why in approach we haven't divided 10* 7 by 2? Are there no repeated handshakes counted?
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vaishnavi2498
I have a doubt, why in approach we haven't divided 10* 7 by 2? Are there no repeated handshakes counted?

Each of the 10 executives shakes hands with each of the 7 chairmen, so it's directly 10 * 7. No need to divide by 2 because there’s no repetition or double counting.

To see this clearly, try picking two small groups, say A, B, C and X, Y, and simply listing all cases. Each of the 3 in the first group shakes hands with each of the 2 in the second group. That's 3 * 2 = 6 handshakes, not 3:

A - X
B - X
C - X
A - Y
B - Y
C - Y
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