Question

Each of eight identical is to be placed in the squares shown in the figures given below in a horizontal direction such that one horizontal row contains six and the other horizontal row contains two *****. In how many maximum different ways can this be done?

(a) 38 (b) 28 (c) 16 (d) 14

Answer 1

There can be two cases:

Case (I) : When x row contains 6 *****:

Then the 2 can be arranged in y row in 6P2 ways = 15 or the 2 can be arranged in any of the 4 two box row in 4 ways.

So, no of ways, when x contains 6 ***** = 15 + 4 = 19.

Case (II) : Similarly, no. of ways, when y row contains 6 ***** = 19

As, either of case (I) or case (II) is possible,

Hence, total no. of ways = 19 + 19 = 38