Respuesta :
Assuming that the topping order is not important, you need to use the combination to solve this question. The number of toppings is 12 and then added 2, so the number will become: 12+2= 14 toppings
From 14 toppings, ian need to choose 3. The possible ways would be:
14C3= 14!/(14-3)!3!= 14*13*12/ 3*2= 364 possible ways
From 14 toppings, ian need to choose 3. The possible ways would be:
14C3= 14!/(14-3)!3!= 14*13*12/ 3*2= 364 possible ways
The number of ways more can Ian choose three toppings if he add two new topping, is 144.
What is arrangement?
Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.
The number of possible ways to arrange is the n!. Here, n is the number of objects.
Sweettooth frozen yogurt has 12 different toppings to choose from. The number of ways he can choose three without considering order is,
[tex]^{12}C_3=\dfrac{12!}{(12-3)!3!}\\^{12}C_3=\dfrac{12\times11\times10\times9!}{9!\times3\times2\times1}\\^{12}C_3=220[/tex]
Now he adds two more toppings. Thus, the number of topping is,
[tex]n=12+2\\n=14[/tex]
Ian choose three toppings from the 14. Let suppose the order of choosing the topping is not important. Thus, the number of ways to choose three toppings from 14 is,
[tex]^{14}C_3=\dfrac{14!}{(14-3)!3!}\\^{14}C_3=\dfrac{14\times13\times12\times11!}{11!\times3\times2\times1}\\^{14}C_3=364[/tex]
Thus, the number of ways more can Ian choose three is,
[tex]364-220=144[/tex]
Hence, the number of ways more can Ian choose three toppings if he add two new topping, is 144.
Learn more about the arrangement here;
https://brainly.com/question/6032811
#SPJ3
