Numberofcombinationsof objectsoftwo types Thenumberofdiﬀerentwaysofordering x objects of onetypeand n − x objects of asecond type in asequence of n objects is given by ! n x - = n! x!(n−x)! . (2) This formulaholdsfor anyinteger valueofxfrom 0ton.The number ' n x , is read ‘n choose x’.Alternative notation for ' n x , is n C x ,sometimes read as ‘n c x’ The number x!isread‘xfactorial’. Forany positiveinteger x,the notation x!isshorthand forthe number 1 × 2 × 3 ×···×x.The number 0! is deﬁnedtobe1

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