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in how many ways can the digits number 8,622,222 be arranged?

Sagot :

The given number is : 8,622,222

Since, there are 7 digits total, Normally the arrangenments of 7 distinct elements are 7!

But in the given number, there are five 2 digit number and one 8 digit number as well as one 6 digit number

From the properties of Permutation: The arrangement of p and q similar elements out of total n elements the arrangements are : n!/p! q!

[tex]\begin{gathered} \text{ Permutation of 8622222=}\frac{7!}{5!} \\ \text{ Permutation of 8622222=}\frac{7\times6\times5!}{5!} \\ \text{ Permutation of 8622222=}\frac{7\times6\times1}{1} \\ \text{ Permutation of 8622222=}42 \end{gathered}[/tex]

Arrangements of 8,622,222 digits are 42

Answer : 42 arrangements