HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 205
The ‘Probability’ group of functions, COMB(<n>, <r>), The ! function
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The 'Probability' group of functions This group of functions is provided to manipulate and evaluate probabilities and probability distribution functions (p.d.f.'s). COMB(,) This function gives the value of nCr using the formula nCr = n! (n − r)!r! . Eg. Find the probability of choosing 2 men and 3 women for a committee of 5 people from a pool of 6 men and 5 women. ⎛6⎞⎛5⎞ p = ⎜ ⎝ 2 ⎟ ⎠ ⎜ ⎝ 3 ⎟ ⎠ = 0.3247 ⎛11⎞ ⎜ ⎝ 5 ⎟ ⎠ Notes: 1. The reason for the single 'COMB(6,2)' above the main calculation is to save time. Rather than using the MATH menu for every entry of the COMB function, you can enter it once and then it repeatedly, changing the parameters each time. 2. For large values of N (>150 or so) it is important to use the COMB function rather than using N!/((N-R)!*R!) because the massive values involved in calculating the factorials will cause inaccuracies internally. The COMB function has internal methods built in which avoid this and give accurate answers. 3. If you are solving for the value of N, such as in a Binomial probability calculation then you must use N!/((N-R)!*R!) rather than COMB. The ! function The factorial function finds the number of possible permutations of an entire collection of n objects. 205
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