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Question Number 111906 by mr W last updated on 05/Sep/20

Answered by PRITHWISH SEN 2 last updated on 22/Sep/20

Disarrangement of 6 cards !6=265 now in this 265 ways card no. 1 can be in envelope no. 2,3,4,5 or 6 and in each case the no. of ways will be same. ∴ The required result will be = (1/5)×265 = 53 ways please check

$$\mathrm{Disarrangement}\:\mathrm{of}\:\mathrm{6}\:\mathrm{cards}\:!\mathrm{6}=\mathrm{265} \\ $$$$\mathrm{now}\:\mathrm{in}\:\mathrm{this}\:\mathrm{265}\:\mathrm{ways}\:\mathrm{card}\:\mathrm{no}.\:\mathrm{1}\:\mathrm{can}\:\mathrm{be}\:\mathrm{in}\: \\ $$$$\mathrm{envelope}\:\mathrm{no}.\:\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\:\mathrm{or}\:\mathrm{6}\:\mathrm{and}\:\mathrm{in}\:\mathrm{each}\:\mathrm{case}\:\mathrm{the} \\ $$$$\mathrm{no}.\:\mathrm{of}\:\mathrm{ways}\:\mathrm{will}\:\mathrm{be}\:\mathrm{same}. \\ $$$$\therefore\:\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{required}}\:\boldsymbol{\mathrm{result}}\:\boldsymbol{\mathrm{will}}\:\boldsymbol{\mathrm{be}}\:=\:\frac{\mathrm{1}}{\mathrm{5}}×\mathrm{265} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{53}\:\boldsymbol{\mathrm{ways}} \\ $$$$\:\:\:\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{check}} \\ $$

Commented by mr W last updated on 22/Sep/20

correct sir!

$${correct}\:{sir}! \\ $$

Commented by PRITHWISH SEN 2 last updated on 22/Sep/20

thank you sir

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

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