Question

How many different signals are possible with 4 blue, 3 red, 2 white and 2green flags by using all at a time in a queue?

Answer 1

Given:

There are flags with different color of 4 blue, 3 red, 2 white and 2 green.

To Find:

How many different signals are possible with 4 blue, 3 red, 2 white and 2 green flags by using all at a time in a queue?

Solution:

Here is total number of flag is given:

Total number of flag = Blue flag's Number+Red flag's Number+White flag's Number+Green flag's Number

Total number of flag = 4 + 3+ 2+ 2 = 11

All these are arranged at a time:

$\mathbf{Number\ of\ signal= \dfrac{!11}{!4\times !3\times !2\times !2}}$

Above can simplify like:

$\mathbf{Number\ of\ signal= \dfrac{11\times 10\times 9\times 8\times 7\times 6\times 5\times !4}{!4\times !3\times !2\times !2}}$

On cancel out !4 in numerator and denominator:

$\mathbf{Number\ of\ signal= \dfrac{11\times 10\times 9\times 8\times 7\times 6\times 5}{ !3\times !2\times !2}}$

Again simplify denominator:

$\mathbf{Number\ of\ signal= \dfrac{11\times 10\times 9\times 8\times 7\times 6\times 5}{ 3\times 2\times 2\times 2}}$

On cancel out common number in numerator and denominator:

$\mathbf{Number\ of\ signal= 11\times 10\times 3\times 7\times 6\times 5}$

Number of signal = 69300

Total 69300 different signals are possible with 4 blue, 3 red, 2 white and 2 green flags by using all at a time in a queue.

Answer 2

Answer:

Step-by-step explanation: