Iff ""^(5)P(r)=""^(6)P(r-1) find r....

Iff `""^(5)P_(r)=""^(6)P_(r-1)` find r.

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If ""^(10)P_(r)=""^(7)P_(r+2) find r.

If ""^(20)P_(r)=13xx""^(20)P_(r-1) find r.

Find r if ""^(5)P_(r)=2""^(6)P_(r-1)

If ""^(nP_(r)=""^(n)P_(r+1) and ""^(n)C_(r)=""^(n)C_(r-1) find n and r.

If ""^(n)P_r = ""^(n)P_(r-1) and ""^(n)C_(r) = ""^(n)C_(r-1) , find the values of n and r.

If ""^(10)P_(r-1) = 2xx ""^(6) P_r, find r.

If .^(10)P_(4)= .^(7)P_(r+2) find r.

FULL MARKS-COMBINATORICS AND MATHEMATICAL INDUCTION-ADDITIONAL QUESTIONS

How many 3-digit numbers can be made using digit 1,2,3,4,6,7 if no dig...
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Find the number of 4-digit numbers that can be formed using the digits...
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Iff ""^(5)P(r)=""^(6)P(r-1) find r.
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How many words, with or without meaning , can be made from the letters...
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A group consists of 4 girls and 7 boys. In how many ways can a team of...
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A committee of 6 is to be choosen from 10 men and 7 women so as to con...
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Using the digits 1,2,3,4,5,6,7 a number of 4 different digits is forme...
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If ""^(22)P(r+1):^(20)P(r+2)=11:52, find r.
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If ""^(nP(r)=""^(n)P(r+1) and ""^(n)C(r)=""^(n)C(r-1) find n and r.
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A committee of 7 peoples has to be formed from 9 men and 4 women . In ...
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In .^(2n)C(3) :.^(n)C(3) = 11 : 1 then n is
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Find the number of ways of selecting 9 balls from 6 red balls, 5 white...
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If 1/(7!)+1/(9!)=x/(10!), find x.
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If ""^(n)C(4),^(n)C(5)" and "^(n)C(6) are in A.P. then find n.
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Prove by induction the inequality (1+x)^(n) ge 1 + nx. whenever x is p...
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Prove that 3^(2n)-1 is divisible by 8.
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Prove that x^n-y^n is divisible by x - y for all positive integers n.
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Prove by mathematical induction that for every natural number n, 3^(2n...
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Use the principle of mathematical induction to prove that for every na...
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n^(3)-n is divisible by 6, for each natural number n ge 2
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