Question

In how many different ways can the numbers '256974' be arranged, using each digit only once in each arrangement, such that the digits 6 and 5 are at the extreme ends in each arrangement?

• A. 48
• B. 720
• C. 36
• D. 360
• E. None of these

Answer 1

The correct option is A 48

Case I
$\begin{array}{cccccc}6& & & & & 5\end{array}$
Four empty places can be filled by the remaining digits 2,9,7 and 4 in 4! ways, i.e
$4\times 3\times 2\times 1=24ways$
Case II
$\begin{array}{cccccc}6& & & & & 6\end{array}$
Similarly, number of arrangenents = 24
$\therefore$ Required number of arrangements
= 24 + 24 = 48