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).