3
Problems(4)
Letters and Envelopes
Source:
3/15/2010
After a typist has written ten letters and had addressed the ten corresponding envelopes, a careless mailing clerk inserted the letters in the envelopes at random, one letter per envelope. What is the probability that exactly nine letters were inserted in the proper envelopes?
probability
Length of an Altitude
Source:
3/16/2010
A triangle has altitudes of length 5 and 7. What is the maximum length of the third altitude?
geometry
Gaussian Prime Factorization
Source:
3/15/2010
A Gaussian prime is a Gaussian integer z\equal{}a\plus{}bi (where and are integers) with no Gaussian integer factors of smaller absolute value. Factor \minus{}4\plus{}7i into Gaussian primes with positive real parts. is a symbol with the property that i^2\equal{}\minus{}1.
A Σ to a Binomial
Source:
3/20/2010
Simplify: \sum\limits_{k \equal{} 10}^{2006} \binom{k}{10} (Your answer should contain no summations but may still contain binomial coefficients/combinations.)