How many signals can be made by hoisting Six Flags?
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Note: Always remember that permutation is rearranging order of elements and permutation is denoted by $^{n}{{P}_{r}}$, where n are total objects and r are numbers of objects taken at a time and is equals to $\dfrac{n!}{\left( n-r \right)!}$. Evaluate each and every case of different numbers of flags hoisted at once carefully. Try not make any calculation mistakes. Show The number of signals that can be sent by 6 flags of different colours taking one or more at a time is 1956. Explanation: Number of signals using one flag = 6P1 = 6 Number of signals using two flags = 6P2 = 30 Number of signals using three flags = 6P3 = 120 Number of signals using four flags = 6P4 = 360 Number of signals using five flags = 6P5 = 720 Number of signals using all six flags = 6P6 = 720 Therefore, the total number of signals using one or more flags at a time is 6 + 30 + 120 + 360 + 720 + 720 = 1956 (Using addition principle). How many signals does Six Flags make?=6P1+6P2+6P3+6P4+6P5+6P6=6+30+120+360+720+720=1956. Q. How many different signals can be given by using any number of flags from six flags of different colors?
How many signals can 4 flags from Six Flags make?Solution : Required number of signals
= number of arrangements of 6 flags taking 4 at a time `= ""^(6)P_(4)=(6xx5xx4xx3)=360. ` How many signals can be made by hoisting 6 differently?Hence, total number of signals =720+720+360+120+30+6=1956 ways.
How many signals can be made by hoisting 4 flags?Answer and Explanation: Thus, 420 different signals are possible.
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