Question 105

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 ?

Solution

Case 1 : 6 at left end and 5 is at right end : 6 _ _ _ _ 5

Now, four empty places can be filled by 2,9,7 and 4 in = $$4!$$ ways

= $$4 \times 3 \times 2 \times 1 = 24$$

Case 2 : 6 at right end and 5 at left end : 5 _ _ _ _ 6

Similarly, no. of ways = $$4!$$

= $$4 \times 3 \times 2 \times 1 = 24$$

$$\therefore$$ Total no. of ways = $$24 + 24 = 48$$

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