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?

Name: 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?
Uploaded: 2022-02-23T17:22:57+00:00
Description: 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?

Question

Wayne Everett · Accepted Answer

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 2You 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.