In how many different ways can the six symbols @, $, $, $, @, and #
[#permalink]
18 Dec 2024, 14:36
We need to find the number of ways the 6 six symbols \(@,\$,\$,\$,@,\&\) be arranged on a straight line.
We know that the number of ways to arrange $\(n\)$ items in a straight line out of which $\(p\)$ are one kind identical, q are another kind identical and rest are all distinct is $\(\frac{\mathrm{n}!}{\mathrm{p}!\mathrm{q}!}\)$
So, using above, the number of ways to arrange 6 symbols \(@, \$,\$,\$,@,\&\) out of which 3 are identical (\$ symbols) and 2 are another kind identical (\(@\) symbols) is $\(\frac{6!}{3!\times 2!}=\frac{6 \times 5 \times 4}{2 \times 1}=60\)$
Hence the answer is (B).