A security code is to be formed using all six letters of the word PLANET, with each letter used exactly once. It is required that the code starts with ‘P’ and ends with ‘T’.

Consider the following statements:
Statement I: The number of such codes is equal to the number of permutations of the remaining letters after fixing the first and last letters.
Statement II: The number of such codes is one-twentieth of the total number of unrestricted six-letter codes that can be formed using the word PLANET.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

A security code is to be formed using all six letters of the word PLANET, with each letter used exactly once. It is required that the code starts with &lsquo;P&rsquo; and ends with &lsquo;T&rsquo;.

Consider the following statements:
Statement I: The number of such codes is equal to the number of permutations of the remaining letters after fixing the first and last letters.
Statement II: The number of such codes is one-twentieth of the total number of unrestricted six-letter codes that can be formed using the word PLANET.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

ONLiNE UPSC · Accepted Answer

Total unrestricted 6-letter permutations of PLANET = 6! = 720
Fixing P at start and T at end: remaining 4 letters &rarr; 4! = 24 codes
Statement I is correct (basic permutation reasoning)
Statement II: 720 &divide; 20 = 36 &ne; 20 &rarr; incorrect
Hence, option a is correct.

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M Question 1	⏱ 0
A security code is to be formed using all six letters of the word PLANET, with each letter used exactly once. It is required that the code starts with ‘P’ and ends with ‘T’. Consider the following statements: Statement I: The number of such codes is equal to the number of permutations of the remaining letters after fixing the first and last letters. Statement II: The number of such codes is one-twentieth of the total number of unrestricted six-letter codes that can be formed using the word PLANET. Select the correct answer from below: (a) Only Statement I is correct. (b) Only Statement II is correct. (c) Both Statements I and II are correct. (d) None of the Statements is correct.