Question

A flag is to be coloured in four stripes by using 6 different colours,no two consecutive stripes being of the same color.This can be done

• A. $1500$ ways
• B. $750$ ways
• C. $6^4$ ways
• D. none of these

Answer 1

The correct option is B $750$ ways

Given,
Four stripes by 6 different colours and no two consecutive stripes should have same colour
=>1st stripe can be be coloured in 6 different ways
2nd stripe should not have the same colour as first then it can be coloured in 5 ways
3rd stripe should not have the same colour as 2nd this can also be coloured in 5 ways
4th stripe should not have the same colour as 3rd so this stripe can be coloured in 5 ways
=> total sum=$6\times 5\times 5\times 5$=750
Hence option B is correct