The number of permutations of letters a, b, c, d, e, f, g so that neither the pattern beg nor cad appears is

Total number of permutations = 7!Let A be the property that ‘beg’ occurs.B be the property that cad occurs.Number of permutations with A = 5!= that of with B and n(A∩B)=3!∴ n(A∪B)=5!+5!−3!=234∴ Required number = 7! – 234 = 4806