How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?

Name: How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?
Uploaded: 2025-11-18T17:06:47.483962+05:30
Duration: 5 min 29 s
Description: How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?

Solution

To make a signpost either we can use 1 symbol or 2 symbols or 3 symbols or 4 symbols or 5 symbols or 6 symbols . When we use "X" particular no of symbols of different colours we can arrange them in $$X!$$ .

Hence total ways = $$6_{P_1}+6_{P_2}+6_{P_3}+6_{P_4}+6_{P_5}+6_{P_6}$$
= 1956.