How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
There are as many codes as there are ways of filling 4 vacant places
in succession by the first 10 letters of the English alphabet, keeping in mind that the repetition of letters is not allowed.
The first place can be filled in 10 different ways by any of the first 10 letters of the English alphabet following which, the second place can be filled in by any of the remaining letters in 9 different ways. The third place can be filled in by any of the remaining 8 letters in 8 different ways and the fourth place can be filled in by any of the remaining 7 letters in 7 different ways.
Therefore, by multiplication principle, the required numbers of ways in which 4 vacant places can be filled is 10 × 9 × 8 × 7 = 5040
Hence, 5040 four-letter codes can be formed using the first 10 letters of the English alphabet, if no letter is repeated.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, – 4) and B (8, 0).
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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Prove that
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
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Give three examples of sentences which are not statements. Give reasons for the answers.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
Name the octants in which the following points lie:
(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)
Thxx