Get 2 FREE Instant-Explanations on Filo with code FILOAPP

{A} is a set containing {n} elements. A subset {P}_{{1}} is ch

Question

$A$ is a set containing $n$ elements. A subset $P_{1}$ is chosen and $A$ is reconstructed by replacing the elements of $P_{1}$ . The same process is repeated for subsets $P_{1}, P_{2}, \dots ., P_{m}$ with $m > 1$ . The number of ways of choosing $P_{1}, P_{2}, \dots ., P_{m}$ so that $P_{1} \cup P_{2} \cup \dots . \cup P_{m} = A$ is (a) $(2^{m} - 1)^{m n}$ (b) $(2^{n} - 1)^{m}$ (c) $(m + n) C_{m}$ (d) none of these

Views: 807 students

Found 6 tutors discussing this question

Liam Discussed

A

is a set containing

n

elements. A subset

P_{1}

is chosen and

A

is reconstructed by replacing the elements of

P_{1}

. The same process is repeated for subsets

P_{1}, P_{2}, \dots ., P_{m}

with

m > 1

. The number of ways of choosing

P_{1}, P_{2}, \dots ., P_{m}

so that

P_{1} \cup P_{2} \cup \dots . \cup P_{m} = A

is (a)

(2^{m} - 1)^{m n}

(b)

(2^{n} - 1)^{m}

(c)

(m + n) C_{m}

(d) none of these

10 mins ago

Discuss this question LIVE