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The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is equal to :
(2) 2520
Five 1s and three 2s fill 8 places, so the other 2 terms are 0s.
Number of arrangements of 1, 1, 1, 1, 1, 2, 2, 2, 0, 0:
10!5! 3! 2! = 3628800120 6 2 = 2520
Answer: (2)
The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is : [figure]
Let P be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in P are formed by using the digits 1, 2 and 3 only, then the number of elements in the set P is :
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The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is .