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You are ordering a hamburger and can get up to 7 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 2 toppings

Mar 5, 2020

#1
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We  can use  the  7th row  of Pascal's Triangle  to  solve  this

Number  of  Toppings         Number  of  Possible Combos

0                                           1

1                                           7

2                                          21

3                                          35

4                                          35

5                                          21

6                                            7

7                                            1

Assuming that  we can choose to have  no toppings.....the probabilty  of two toppings =

21 / 2^7  =   21/ 128

However...if we  must have at least  one topping the probability  of getting two toppings  =

21 / [ 2^7 - 1]  =    21/  127

Mar 5, 2020