Question 1079188
C( 9,3 ) = {{{ 9! / ( 3!*( 9 -3 )! ) }}}
C( 9,3 ) = {{{ 9! / ( 3!*6! ) }}}
C( 9,3 ) = {{{ ( 7*8*9 ) / ( 1*2*3 ) }}}
C( 9,3 ) = {{{ 504/6 }}}
C( 9,3 ) = {{{ 84 }}}
84 combinations are possible with 3 toppings
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You also might have 2 toppings:
C( 9,2 ) = {{{ 9! / ( 2!*( 9 -2 )! ) }}}
C( 9,2 ) = {{{ 9! / ( 2!*7! ) }}}
C( 9,2 ) = {{{ ( 8*9 ) / 2! }}}
C( 9,2 ) = {{{ 36 }}}
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You might have 1 topping:
C( 9,1 ) = {{{ 9! / ( 1!*( 9-1 )! ) }}}
C( 9,1 ) = {{{ 9! /  8! }}}
C( 9,1 ) = {{{ 9 }}}
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Adding up the combinations:
{{{ 84 + 36 + 9 = 129 }}} possible
( get another opinion if needed )