You can make your own pizza and choose up to 4 toppings from a list of 10. You c

Question

You can make your own pizza and choose up to 4 toppings from a list of 10. You can choose one topping multiple times (you will get more of it on your pizza). You can also choose less than 4 toppings or no toppings at all. How many different pizzas can you create? What about choosing up to k toppings from a list of n? Donald Duck's family picture Donald Duck, Daisy Duck, Uncle Scrooge, Huey, Dewey, and Louie are taking a family picture together. In how many different ways can they arrange themselves forming a line in the picture? It happens that Huey, Dewey, and Louie are a triplet of identical siblings and are all wearing the same color T-shirt and cap. So they cannot be distinguished in the picture. In how many different ways can they arrange themselves to form a line assuming that Huey, Dewey, and Louie are completely undistinguishable?

Explanation / Answer

a) as number of pizzas with 0 toppings =1

number of pizzas with 1 topping =10 ; as we have 10 choices

number of pizzas with 2 topping =102=100 ; as we have 10 choices for each topping

number of pizzas with 3 topping =103 =1000 ; as we have 10 choices for each topping

number of pizzas with 3 topping =104 =10000 ; as we have 10 choices for each topping

total number of pizzas =1+10+100+1000+10000 =11111

b) as each topping has n choices . hence total number of toppings =kn

1.2) as there are 6 people for first we have 6 choices of place to put him, for second 5, third 4 and so on.

hence wat to arrange them =6*5*4*3*2*1=720

b) as three people are indistingushable, their own permutation should be discarded,

hence number of ways =6!/3! =120

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