Q. In how many ways may a college president's wife invite two or more of eight faculty wives to a tea?
Since it is two or more , inviting one must be excluded . Therefore , the answer would be $\binom{8}{8}-\binom{8}{1}$ . Am I correct?
Asked
Active
Viewed 825 times
0
-
What do you mean by two or more? – QuIcKmAtHs Jan 04 '18 at 11:28
-
3You do realise your answer is negative? – jonsno Jan 04 '18 at 11:28
2 Answers
0
We need to compute $\sum_{n=2}^{8} {8\choose n} = \sum_{n=0}^{8} {8\choose n} - {8\choose 1} - {8\choose 0} = 2^8-9$
Dan
- 382
0
You must know that the number of ways of choosing two people from $8$ is given by $\binom82$. Similarly, we can calculate the rest.
Hence, our answer is: $$P = \binom82 + \binom83 + \ldots + \binom88 = 2^8 - \binom81 - \binom80 = 2^8-9 = 247$$
Note that $$\sum_{i=0}^{n} \binom {n}{i} = 2^n $$