Question

There are 35 students and 04 teachers. In how many ways every student shakes hand with other students and all the teachers.

Answer 1

To find the total number of handshakes between students and teachers, you can calculate the handshakes separately for students and teachers, and then add them together.

For students:

There are 35 students, and each student shakes hands with every other student exactly once (since shaking hands is a mutual interaction). You can use the combination formula to calculate this:

Number of student handshakes = C(35, 2) = 35! / (2! * (35 - 2)!)

= (35 * 34) / 2

= 595

For teachers:

There are 4 teachers, and each teacher shakes hands with every student exactly once. So, the number of teacher-student handshakes is 4 * 35 = 140.

Total number of handshakes = Student handshakes + Teacher-student handshakes

= 595 + 140

= 735

There are 735 ways for students to shake hands with each other and with all the teachers.