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Show that the total number of permutatio...

Show that the total number of permutations of n diferent things not more than r things at a time (repetition being allowed) is `(n(n^(r)-1))/(n-1)`.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
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  2. Examine the validity of the following statement: If a and b ar odd i...

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  3. Show that the total number of permutations of n diferent things not mo...

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  4. A and B stand in a line with 10 other people. In how many of the perm...

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  5. Find the number of permutations of the letters x,x,x,y,y,y,z,w taken 5...

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  6. A bag contains 50 tickets 1,2,3,...50 of which 5 are drawn at random a...

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  7. In n gt 7 prove that ""^(n-1)C(3)+""^(n-1)C(4) gt ""^(n)C(3)

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  8. If (""^(n)C(r-1))/(a)=(""^(n)C(r))/(b)=(""^(n)C(r))/(c) prove that n=(...

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  9. A,B and C have respectively 4,3 and 2 differrent books. In how many d...

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  10. Find the modulus and ampltidue of the complex in numberz=(-2-i2 sqrt(3...

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  11. Find the amplitude of z=1+i "tan" (3pi)/(5)

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  12. Find the modulus and amplitude of z="sin" (6pi)/(5)+I (1+"cos" (6pi)...

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  13. There are m A.P. Whose common differences are 1,2,3,.. M respectively...

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  14. If S(1),S(2),S(3),...S(m) be the sum of first n terms of n A.P. Whose...

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  15. Show that the sum of the numbers in the n th bracket of the series (1)...

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  16. Show that the following two A.P. is have 14 common terms 3,7,11,15...,...

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  17. Show that there are 17 identical terms in the following two A.P. 2,5,8...

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  18. Find the n th term and the sum of first n terms of thefollowing sequen...

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  19. Solve |x^(2)+4x+3|+2x+5=0

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  20. For a gt0, determine all the roots of the equations x^(2)-2a|x-a|-3a...

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