91Ó°ÊÓ

List all the combinations of 5 objects \(a, b, c, d,\) and \(e\) taken 2 at a time. What is \(C(5,2) ?\)

In a survey of 100 investors in the stock market, 50 owned shares in IBM 40 owned shares in AT\&T 45 owned shares in GE 20 owned shares in both IBM and GE 15 owned shares in both \(\mathrm{AT} \& \mathrm{~T}\) and \(\mathrm{GE}\) 20 owned shares in both IBM and AT\&T 5 owned shares in all three (a) How many of the investors surveyed did not have shares in any of the three companies? (b) How many owned just IBM shares? (c) How many owned just GE shares? (d) How many owned neither IBM nor GE? (e) How many owned either IBM or AT\&T but no GE?

Human blood is classified as either \(\mathrm{Rh}+\) or \(\mathrm{Rh}-.\) Blood is also classified by type: \(\mathrm{A},\) if it contains an A antigen but not a \(B\) antigen; \(B\), if it contains a \(\mathrm{B}\) antigen but not an \(\mathrm{A}\) antigen; \(\mathrm{AB},\) if it contains both \(\mathrm{A}\) and \(B\) antigens; and \(O\), if it contains neither antigen. Draw a Venn diagram illustrating the various blood types Based on this classification, how many different kinds of blood are there?

How many two-letter codes can be formed using the letters \(A, B, C,\) and \(D ?\) Repeated letters are allowed.

How many two-letter codes can be formed using the letters \(A, B, C, D,\) and \(E\) ? Repeated letters are allowed.

How many three-digit numbers can be formed using the digits \(0,1,2,3,4,5,6,7,8,\) and \(9 ?\) Repeated digits are allowed.

An urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles. If one marble is selected, determine the probability that it is black.

Assume equally likely outcomes. Determine the probability of having 3 boys in a 3 -child family.

How many different four-letter codes are there if only the letters \(A, B, C, D, E,\) and \(F\) can be used and no letter can be used more than once?

Assume equally likely outcomes. Determine the probability of having 3 girls in a 3 -child family.