How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
Solution and Explanation
It is given that the 5-digit telephone numbers always start with 67.
Therefore, there will be as many phone numbers as there are ways of filling 3 vacant places 
by the digits 0 - 9, keeping in mind that the digits cannot be repeated.
The units place can be filled by any of the digits from 0 - 9, except digits 6 and 7. Therefore, the units place can be filled in 8 different ways following which, the tens place can be filled in by any of the remaining 7 digits in 7 different ways, and the hundreds place can be filled in by any of the remaining 6 digits in 6 different ways.
Therefore, by multiplication principle, the required number of ways in which 5-digit telephone numbers can be constructed is 8 x 7 x 6 = 336
Top Questions on permutations and combinations
Match List-I with List-II
List-I List-II (A) \(^{8}P_{3} - ^{10}C_{3}\) (I) 6 (B) \(^{8}P_{5}\) (II) 21 (C) \(^{n}P_{4} = 360,\) then find \(n\). (III) 216 (D) \(^{n}C_{2} = 210,\) find \(n\). (IV) 6720
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Questions Asked in CBSE Class XI exam
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.- CBSE Class XI
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Find the mean deviation about the median for the data
xi 15 21 27 30 35 fi 3 5 6 7 8 - CBSE Class XI
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- ‘Have you come back?’ said the woman. ‘I thought that no one had come back.’ Does this statement give some clue about the story? If yes, what is it?
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.