Let S denote the 10-element set {a,b,c,d,e,f,g,h,i,j}. How manyways can we construct a subset of S of size 7 ? 120 How many wayscan we construct a subset of S of size 7 containing the element j?84 How many ways can we construct a subset of S of size 7containing i but not j ? 28 How many ways can we construct a subsetof S of size 7 containing h but neither i nor j ? 7 How many wayscan we construct a subset of S of size 7 containing g but not h, ior j? 1 Note that every subset of S of size 7 falls into exactlyone of the categories described in parts (b) through (e) above. Usethat fact to derive a summation formula involving expressionsnCr.
