Question

(5C0)(50C6)-(5C1)(40C6)+(5C2)(30C6)-(5C3)(20C6)+(5C4)(10C6)​

Answer 1

Given: (5C0)(50C6)-(5C1)(40C6)+(5C2)(30C6)-(5C3)(20C6)+(5C4)(10C6)​

To find: Solve the above combination.

Solution:

• So, to solve this combination we have the formula:

            a C 2b = a !  / ( a− b ) ! b !

• So, by using this formula, we get:

           = 5 !  / ( 5− 0 ) ! 0 ! x 50 !  / ( 50− 6 ) ! 6 !  -  5 !  / ( 5− 1 ) ! 1 ! x 40 !  / ( 40− 6 ) ! 6 !  +  5 !  / ( 5− 2 ) ! 2 ! x 30 !  / ( 30− 6 ) ! 6 !  -  5 !  / ( 5− 3 ) ! 3 ! x 20 !  / ( 20− 6 ) ! 6 !  +  5 !  / ( 5− 4 ) ! 4 ! x 10 !  / ( 10− 6 ) ! 6 !

• Now simplifying the terms step by step we get:

          = 15890700 - 5(3838380) + 10(593775) - 10(38760) + 5(210)

          =  15890700 - 19191900 + 5937750 - 387600 + 1050

         =  2250000

Answer:

           So the value of the combination is 2250000.