<prompt> Ikiwa x ni nambari halisi na k sio nambari kamili, kumbuka kwamba mgawo wa binomial binomxk unafafanuliwa na fomula. binomxk fracxx - 1x - 2 dots x - k 1k! , .Hesabu thamani ya fracbinom122014 cdot 42014binom40282014 , .  <response>: beginaligned binom122014 frac1212-112-2dotsm12-2014 1 2014! frac12-12-32dotsm-402522014! frac-1-3dotsm-40252014!22014 -frac13dotsm40252014!22014 cdot frac2cdot4cdot6cdotdotscdot 40262 cdot4cdot6cdotdotscdot 4026 -frac4026! 2014!2201420132013! mwishoalignedHivyo basibeginaligned fracbinom122014cdot 420144028 chagua 2014 -frac4026!cdot 42014 2014!2201420132013!4028 chagua 2014 -frac4026!cdot 240282014!2014! 2014!240272013!4028! -frac1 4027. mwishoimepangiliwa 