Assertion :If p, q < r, the number of different selections of p+q things taking r at a time, where p things are identical and q other things are identical, is $p + q - r + 1$ . Reason: If p, q > r, the number of different selections of p+q things taking r at a time, where p things are identical and q other things are identical, is r-1.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is C Assertion is correct but Reason is incorrect
Statement A:
Case number Selection from p Selection from q
1 p r-p
2 p-1 r-p+1
... ... ...
p-r+q r-q+1 q-1
p-r+q+1 r-q q
Thus, total cases = $p + r - q + 1 = p + q - r + 1$
Statement II:
Case number Selection from p Selection from q
1 r 0
2 r-1 1
... ... ...
r 1 r-1
r+1 0 r
Thus, total cases = $r + 1$
Hence, Statement I is correct and Statement II is wrong.
Hence, (c) is correct.

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Similar questions

Q. If r > p > q, the number of different selections of p + q things taking r at time, where p things are identical and q other things are identical, is

Q. Assertion :A bag contains 10 balls in which 3 are identical, then number of ways of selecting 6 balls from the bag is

^{8} C_{2} +^{8} C_{4}

Reason: If a lot has n things out of which p are identical then number of ways of selecting r things from the lot is

r \sum r = r - p

^{n - p} C_{r}

r > p .

Q. Assertion (A)
At point P of a circle with centre O and radius 12 cm, a tangent PQ of length 16 cm is drawn. Then, OQ = 20 cm.

Reason (R)
The tangent at any point of a circle is perpendicular to the radius through the point of contact.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

Q. Column-I contains four statements following reason and Column-II consists of four options (P,Q,R,S)

P \to

- If both statement and reason are true and reason is correct explanation of statement.

Q \to

-If both statement and reason are true and reason is not correct explanation of statement.

R \to

- If statement is correct and reason is incorrect.

S \to

- If both statement and reason are incorrect.

Assertion (A) Phenols give o-and p-nitrophenol on nitration with conc. $H N O_{3} a n d H_{2} S O_{4}$ mixture.
Reason (R) - OH group in phenol is o-,p-directing.
(a) Assertion and reason both are correct and reason is correct explanation of assertion.
(b) Assertion and reason both are wrong statements.
(c) Assertion is correct statement but reason is wrong statement.
(d) Assertion is wrong statement but reason is correct statement.
(e) Both assertion and reason are correct statements but reason is not correct explanation of assertion.

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Case number	Selection from p	Selection from q
1	p	r-p
2	p-1	r-p+1
...	...	...
p-r+q	r-q+1	q-1
p-r+q+1	r-q	q