(A) 28 Calcule: a) 61 d) 3!-2! b) 4! e) 7!-5! c) 0!+1! f) 5cdot 3! (4) 29 Obtenha o valor de cada uma das expressões seguintes: a) (8!)/(6!) d) (7!)/(5!cdot 2!) b). (9!)/(10!) e) (20!)/(18!cdot 2!) (3!)/(4!)+(4!)/(5!) f) (8!cdot 6!)/(7!cdot 7!) (3) 30 Efetue: a) (11!+9!)/(10!) c) (40!-39!)/(41!) b) 17!-17cdot 16! d) ((85!)^2)/(86!cdot 83!)

Vamos calcular cada uma das expressões:<br /><br />(1) 28 Calcule:<br />a) \(6!\) = 720<br />b) \(4!\) = 24<br />c) \(0! + 1!\) = 1 + 1 = 2<br />d) \(3! - 2!\) = 6 - 2 = 4<br />e) \(7! - 5!\) = 5040 - 120 = 4920<br />f) \(5 \cdot 3!\) = 5 \cdot 6 = 30<br /><br />(2) 29 Obtenha o valor de cada uma das expressões:<br />a) \(\frac{8!}{6!}\) = \(\frac{40320}{720}\) = 56<br />b) \(\frac{9!}{10!}\) = \(\frac{362880}{3628800}\) = \(\frac{1}{10}\)<br />c) \(\frac{3!}{4!}\) + \(\frac{4!}{5!}\) = \(\frac{6}{24}\) + \(\frac{24}{120}\) = \(\frac{1}{4}\) + \(\frac{1}{5}\) = \(\frac{5}{20}\) + \(\frac{4}{20}\) = \(\frac{9}{20}\)<br />d) \(\frac{7!}{5! \cdot 2!}\) = \(\frac{5040}{120 \cdot 2}\) = \(\frac{5040}{240}\) = 21<br />e) \(\frac{20!}{18! \cdot 2!}\) = \(\frac{3628800}{720 \cdot 2}\) = \(\frac{3628800}{1440}\) = 2520<br />f) \(\frac{8! \cdot 6!}{7! \cdot 7!}\) = \(\frac{40320 \cdot 720}{5040 \cdot 5040}\) = \(\frac{29030400}{25401600}\) = \(\frac{115}{102}\)<br /><br />(3) 30 Efetue:<br />a) \(\frac{11! + 9!}{10!}\) = \(\frac{39916800 + 362880}{3628800}\) = \(\frac{40286400}{3628800}\) = 11<br />b) \(17! - 17 \cdot 16!\) = 355687428096000 - 17 \cdot 20922789888000 = 355687428096000 - 355687428096000 = 0<br />c) \(\frac{40! - 39!}{41!}\) = \(\frac{518918400388080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000