How many ternary strings of length 10 that contain exactly 2 1s and 3 2s....

Alexandra Richardson

Alexandra Richardson

Answered

2022-07-16

How many ternary strings of length 10 that contain exactly 2 1s and 3 2s. Since it must contain exactly 2 1s and 3 2s the other 5 spaces must be 0s.But how many ways can we arrange this?

Answer & Explanation

Wayne Everett

Wayne Everett

Expert

2022-07-17Added 19 answers

Step 1
( 2 10 ) × ( 3 8 ) = 10 ! 2 ! ( 10 8 ) ! 8 ! 3 ! ( 8 3 ) ! = 10 ! 2 ! 3 ! 5 !
(using classical formula ( n p ) = n ! p ! ( n p ) ! .)
Step 2
You first choose the 2 places (among 10) where you place the 1s, then, for each of these choices, you can select the 3 places where you will place a 2 (in each case among the remaining 8 places). No more choices for the other places where the zeros will be placed.

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