Can you help me with this? Permutation ....

In how many ways can 6 mathematics and 3 design books is arranged on a half if design books are not to be separated?

#Permutation

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

See, Let there be a case in which the three design books are on one side of the shelf covering three out of nine places. Now, the ways to arrange those three design books is 3! = 6 and the number of ways to arrange the rest of the mathematics books is 6!. So total ways are 6! x 3! = 4320. But the set of three design books can be moved to different 3 places instead of the first three. So total ways are 7 x 4320= 30240.

A Former Brilliant Member - 6 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$