Question

Discrete Math

Question 1:

Answer the following questions using your knowledge of binomial coefficients. Imagine a committee comprised of 7 men and 8 women.

a) How many ways can you choose single representative from the committee?

b) How many ways can you choose a task force of 3 members from the committee?

c) How many ways can you choose a task force of 3 members who will then fit three roles: task force leader, task force vice-leader and task force scribe?

Question 2:

Later today is the first meeting of the Super Awesome Club for Super Awesome People, at which every pair of the 54 members must perform the secret handshake.

a) Using your knowledge of binomial coefficients to find out how many handshakes will occur at the meeting.

b) A camera recording the meeting sees the first member walk in and see nobody, so no handshakes occur. Then the second member walks in, and shakes hands with the first member (now 0+1 handshakes have occurred). Next, the third member walks in and shakes each already-present-member's hand. The question: How many hands will the last (54th) member shake?

c) Express part (b) as a summation, and find the total using a formula.

Question 3:

Simplify the expression (n

2) to an expression which has no binomial coefficients and no factorials. To do so, you should use the provided formula:

(

n

k

) = n! / k!(n-k)!

b)Now similarly simplify the expression (n

3).

c) Lastly, use your answer to part (a) to prove that 2. (m (m

2) +. 1) = m^{2.(Show that one side is equal to the other side, do not start with this equation to prove itself).}

Answer 1

Any query then comment below..

Accorsing to rules and regulation , we are able to do only one question at a time.. i provide you the solution of 2 questions..

a) to choos we have b) hoos e ó ne 273- a) Tota Shake hord 143) menber sha ke hord with s 3