Find the number of ways in which ten things, of which $4$ are alike, can be arranged in a circular order?

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Solution

Number of ways $= \frac{10!}{\frac{2 \times 10}{4!}}$
$\begin{matrix} = \frac{10!}{2 \times 10 \times 4!} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4!}{2 \times 10 \times 4!} = 7560 w a y s . \end{matrix}$

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Find the number of ways in which ten things, of which 4 are alike, can be arranged in a circular order?

Number of ways =10!2×104!=10!2×10×4!=10×9×8×7×6×5×4!2×10×4!=7560ways.

Find the number of ways in which ten things, of which $4$ are alike, can be arranged in a circular order?

Number of ways $= \frac{10!}{\frac{2 \times 10}{4!}}$
$\begin{matrix} = \frac{10!}{2 \times 10 \times 4!} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4!}{2 \times 10 \times 4!} = 7560 w a y s . \end{matrix}$