Question 221683
My approach would be
How many possible 3 toppings are there?
Combinations of 14 things taken 3 at a time
(1) {{{14!/(3!*(14-3)!)}}}
How many 3 toppings are just veggie?
Combinations of 8 things taken 3 at a time 
(2) {{{8!/(3!*(8-3)!)}}}
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The probability of getting 3 toppings just veggie
is (2) divided by (1)
(1) {{{14!/(3!*(14-3)!)}}}
(1) {{{14!/(3!*11!)}}}
(1) {{{12*13*14 / (3*2*1)}}}
(1) {{{2184/6}}}
(1) {{{364}}}
and
(2) {{{8!/(3!*(8-3)!)}}}
(2) {{{8!/(3!*5!)}}}
(2) {{{8*7*6/(3*2*1)}}}
(2) {{{336/6}}}
(2) {{{56}}}
Probability 3 toppings are veggie
{{{56/364 = 2/13}}}
Hope I got it