Question

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 $\sum _{r=r-p}^r$ ${}^{n-p}{C}_r$ if $r>p.$

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A),
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A)is true but (R) is false.
• D. (A)is false but (R) is true.

Answer 1

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A),

Given $n=10,P=3,r=6(r\ge p)$

$\therefore$ Required number of ways $=\sum _{r=6-3}^6$ ${}^7{C}_r$ $\sum _{r=3}^6$ ${}^7{C}_r$ ${=}^7{C}_3{+}^7{C}_4{+}^7{C}_5{+}^7{C}_6{=}^8{C}_4{+}^8{C}_6{=}^8{C}_2{+}^8{C}_4$

$\therefore$ Choice (A) is true as Reason is correctly defined & Assertion is correct.