tHE NO. OF DIFFERENT SIGNALS CAN BE GIVEN USING ANY NUMBER OF FLAGS FROM 4flags of different colour is?

The answer is given as 64.

Plz.explain...

signals using one flag = 4

signals using two flags = (4C2)(2!) .... 4C2-for choosing 2 flags and 2! for their arrangment

signals using three flags = (4C3)(3!)

signals using four flags = (4C4)(4!) 

adding all up gives 64  

Approved

In giving a signal, the order of the placement of colours is important,i.e a red and blue signal is different than the blue and red signal. Hence the order is very important.

Therefore the required no. of ways=⁴P_{1 +}⁴P_{2 +}⁴P_{3 +}⁴P₄ =4+12+24+24=64

Approved