Question

Say you’re an electrical engineer designing an electromechanical subassembly for use in a larger aircraft system. Twelve components are to be stacked into a cylindrical casing in a manner that minimizes the impact of shocks. One end of the casing is designated as the bottom, and the other end is the top. a. If all components are different, how many different design configurations are possible? b. If seven components are identical to one another, but the others are different, how many different design configurations are possible? c. If three components are of one type and identical to each other, and four components are of another type and identical to each other, but the others are different, how many different design configurations are possible?

Answer 1

answer:

given data ,

• the stacked into as the  cylindrical casing is in the  manner that minimizes the impact of shocks are as the haved components is 12

( a ) to find the how many different design of the  configurations are possible is ....?

the probability is show in the below step by step,

here we are know as the total is 12

now the probability is 12!

12*11*10*9*8*7*6*5*4*3*2*1

479001600

therefore the probability is 479001600 ways  

479001600

( b ) to find the  different design of configurations are the possible​​​​​​​ is 7 is .....?

the probability is show in the below step by step,

here we are know as the total is 12

now the probability is writes as the  12! / 7!

now we are using to the factorial formula is n! / r!

now substitute the values is in the above formula

12! / 7!

479001600 / 5040

95040

therefore the probability is 95040

95040

( c ) to find the 3 and 4 identical  components of the design configurations are possible is ..?

the probability is show in the below step by step,

here we are know as the total is 12

now the probability is writes as the  12! , 3! and 4!

now we are using to the factorial formula is n! / r! 1* r! 2

now substitute the values is in the above formula

12! / 3! * 4!

479001600/ 6 * 24

479001600 / 144

3326400

therefore the probability is 3326400

3326400