All the letters of the word ANIMAL are permut | vedclass

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(D) First,we find the rank of the word $ANIMAL$. The letters are $A, A, I, L, M, N$. Arranging them alphabetically: $A, A, I, L, M, N$.Rank calculatio

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$ESORNP$

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(D) First,we find the rank of the word $ANIMAL$. The letters are $A, A, I, L, M, N$. Arranging them alphabetically: $A, A, I, L, M, N$.Rank calculation:$AA... : 4! = 24$$AI... : 4! = 24$$AL... : 4! = 24$$AM... : 4! = 24$$ANA... : 3! = 6$$ANIA... : 2! = 2$$ANIL... : 2! = 2$$ANIMAL : 1$Sum $= 24+24+24+24+6+2+2+1 = 107$. So,$x = 107$.Now,for the word $PERSON$,the letters are $E, N, O, P, R, S$. Arranging them alphabetically: $E, N, O, P, R, S$.We need the $107^{th}$ word:$EN... : 4! = 24$$EO... : 4! = 24$$EP... : 4! = 24$$ER... : 4! = 24$Total so far $= 96$.$ESN... : 3! = 6$ (Total $102$)$ESON... : 2! = 2$ (Total $104$)$ESOP... : 2! = 2$ (Total $106$)$ESORNP : 1$ (Total $107$)Thus,the $107^{th}$ word is $ESORNP$.

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