What will be the number of ways to arrange 10 elements out of which 6 are repeated. 720 5040 1000 10!

Question

What will be the number of ways to arrange 10 elements out of which 6 are repeated.
720
5040
1000
10!

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Liliana 2 weeks 2021-10-05T06:10:46+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-05T06:12:02+00:00

    Answer:

    We can solve this task in 2 ways:

    We can choose 1 letter at a time and see in how many ways can it be chosen.

    First letter can be chosen from all  

    10

    , next from  

    9

    , third from  

    8

    and so on until you have only one letter left.

    So the number of ways to arrange the letters can be calculated as:

    n

    =

    10

    ×

    9

    ×

    8

    ×

    7

    ×

    6

    ×

    5

    ×

    4

    ×

    3

    ×

    2

    ×

    1

    =

    3

    ,

    628

    ,

    1000

    Other way can be to treat the possible arrangement as a permutation of  

    10

    element set. The number of permutations can be calculated as:

    P

    n

    =

    n

    !

    =

    1

    ×

    2

    ×

    ×

    n

    Step-by-step explanation:

    0
    2021-10-05T06:12:38+00:00

    720What will be the number of ways to arrange 10 elements out of which 6 are repeated.

    720

    5040

    1000

    10!

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