The number of terms in the expansion of (2x + 3y − 5z)

8 is
(a) C(10, 8) (b) C(11, 8) (c) C(10, 3)​

1 thought on “The number of terms in the expansion of (2x + 3y − 5z)<br /><br />8 is<br />(a) C(10, 8) (b) C(11, 8) (c) C(10, 3)​”

1. SOLUTION

   TO CHOOSE THE CORRECT OPTION

   The number of terms in the expansion of

   [tex] \sf{ {(2x + 3y – 5z)}^{8} }[/tex] is

   (a) C(10, 8)

   (b) C(11, 8)

   (c) C(10, 3)

   EVALUATION

   We know that the number of terms in the expansion of

   [tex] \sf{ {(x_1 + x_2 + … + x_r)}^{n} }[/tex] is

   [tex] \sf{ {}^{n + r – 1}C_{r – 1} }[/tex]

   Here the given expansion is

   [tex] \sf{ {(2x + 3y – 5z)}^{8} }[/tex]

   So r = 3 & n = 8

   Hence the number of terms

   [tex] \sf{ = {}^{8 + 3- 1}C_{3 – 1} }[/tex]

   [tex] \sf{ = {}^{10}C_{2} }[/tex]

   [tex] \sf{ = {}^{10}C_{10 – 2} \: \: \bigg( \because \: \:{}^{n}C_{r} = {}^{n}C_{n – r} \: \bigg) }[/tex]

   [tex] \sf{ = {}^{10}C_{8} }[/tex]

   [tex] \sf{ =C(10,8) }[/tex]

   FINAL ANSWER

   Hence the correct option is (a) C(10, 8)

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