Section 1
Test exercise F.7
How many combinations are there of 6 different numbersFrames selected from the numbers 1 to 49 if the order in which the selection is made does not matter?
Find the value of:(a) 8 !(b) $10 !$(c) $\frac{17 !}{14 !}$(d) $(15-11) !$(e) $\frac{4 !}{0 !}$
Evaluate each of the following:(a) ${ }^{8} C_{3}$(b) ${ }^{15} C_{12}$(c) ${ }^{159} C_{158}$(d) ${ }^{204} \mathrm{C}_{0}$
Expand $(2 a-5 b)^{7}$ as a binomial series.
In the binomial expansion of $(1+10 / x)^{10}$ written in terms of descending powers of $x$, find:(a) the 8th term(b) the coefficient of $x^{-8}$
Evaluate:(a) $\sum_{r=1}^{45} r$(b) $\sum_{r=1}^{n}(9-3 r)$
Determine the 5th term and the sum of the first 20 terms of the series: $1+3+5+7+\ldots$
Using the series expansion of $e^{x}$ find $e^{-2}$ accurate to 3 decimal places.