Q8Single correct4 Marks3 Sep 2023Find the number of ways in which the letters of the word "ARRANGEMENT" can be arranged.A11! / 8!B11! / 16C11! / 7!D7!Weidentifyandcounttherepeatingletters:−A:2times−R:2times−N:2times−E:2times−G:1time−M:1time−T:1timeUsingthepermutationsformulaforrepeatedobjects,thetotalnumberofuniquearrangementsis:11!/(2!⋅2!⋅2!⋅2!⋅1!⋅1!⋅1!)=11!/(2⋅2⋅2⋅2)=11!/16.7! We identify and count the repeating letters: - A: 2 times - R: 2 times - N: 2 times - E: 2 times - G: 1 time - M: 1 time - T: 1 time Using the permutations formula for repeated objects, the total number of unique arrangements is: 11! / (2! \cdot 2! \cdot 2! \cdot 2! \cdot 1! \cdot 1! \cdot 1!) = 11! / (2 \cdot 2 \cdot 2 \cdot 2) = 11! / 16.7!Weidentifyandcounttherepeatingletters:−A:2times−R:2times−N:2times−E:2times−G:1time−M:1time−T:1timeUsingthepermutationsformulaforrepeatedobjects,thetotalnumberofuniquearrangementsis:11!/(2!⋅2!⋅2!⋅2!⋅1!⋅1!⋅1!)=11!/(2⋅2⋅2⋅2)=11!/16.
