Let the number be 10x + y.∴ x + y = 12 ...........(i)10x + y - (10x + x) = 18or 10x + y - 10y - x = 18or 9x - 9y = 18∴ x - y = 2From (i) and (ii), x = 7, y = 5∴ Number = 75
Let the consecutive odd number be x, x + 2, x + 4 and x + 6 respectively.According to the question x + x + 2 + x + 4 + x + 6 = 104 = 4x + 12 = 104 = 4x = 104 - 12 = 92∴ x = 92/4 = 23∴ Required number = x + 4= 23 + 4 = 27
Let the number be 10x + y.Therefore, x + y = 9 ..................(i)10x + y - (10y + x) = 4510x + y - 10y - x = 45Therefore, x - y = 5 ..................(ii)From (i) and (ii), x = 7, y = 2Number = 72Therefore, = x x y = 7 x 2 = 14
There are total eight letters ∴ n(S) = 8PB = 8!As all vowels should come together we assume them as one letter. Here E, I, O and U together are taken as one, so the number of letter is 4 + 1 = 5 and it can be arranged in 5P5 = 5! ways and the vowels can be arranged in 4! ways among themselves∴ n(E) = 4! x 5!∴ P(E) = 4!5! / 8! = 4x3x2x5! / 8x7x6x5! = 4x3x2 / 8x7x6 = 1/14
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