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If all the arrangements formed using aU the letters of the following words are arranged In the order of dictionary then what will be the rank of that word?

(1 ) PINTU

(2) NURI

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(1 ) PINTU

There are 5 letters I I. N, T, U in the word PINTU.

These 5 letters can be arrange in 5P5 = 5! = 120 ways.

Now, we have to obtain the order of the word PINTU from all 120 arrangements as per thern dictionary order.

Alphabetical order of all the letters of the word PINTU is I, N, P T, U.

Number of words with I at the first place

1P1 × 4P4 = 24

Number of words with N at the first place
1P1 × 4P4 = 24

Number of words with P at the first place, I at the second place. N at the third place. T at the fourth place and U at the fifth place = 1P1 × 1P1 × 1P1 × 1P1 × 1P1 = 1 and that word is PINTU itself.

∴ Dictionary order of the word PINTU

= 24 + 24 + 1 = 49.

(2) NURI

‘There are 4 letters N. U, R, I in the word NURI.
These 4 letters can be arrange In 4P4 = 4! = 24 ways.

Now, we have to obtain the order of the word NURI from all 24 arrangements as per the dictionary order.
Alphabetical order of all the letters of the word NURI is I. N. R, U.

Number of words with I at the first place = 1P1 × 3P3 = 3! = 6

Number of words with N at the first place and I at the second place

1P1 × 1P1 × 2P2 = 1 × 1 × 2! = 2

Number of words with N at the first place and R at the second place

1P1 × 1P1 × 2P2 = 1 × 1 × 2! = 2

Number of words with N at the first place, U at the second place and I at the third place = 1P1 × 1P1 × 1P1 × 1P1 = 1.

Now, the word with N at the first place, U at the second place, R at the third place and I at the fourth place is the word NURI itself.

∴ Dictionary order of the word NURI = 6 + 2 + 2 + 1 + 1 = 12

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