Aptitude Discussion

Q. |
How many subsets of {1, 2, 3, ... , 11} contains at least one even integer? |

✖ A. |
1900 |

✖ B. |
1964 |

✔ C. |
1984 |

✖ D. |
2048 |

**Solution:**

Option(**C**) is correct

Given, set = {1,2,3,........,11}

The total number of subsets $=2^{11}$

The number of subsets which contains no even number = 26

The number of subsets which contains at least one even number

$\Rightarrow 2^{11}–2^{6}=2048−64=1984$

**Pragya**

*()
*

cases to select odd no. : 2^6

cases to select even no. : 2^5

removing the case when no even is selected: 2^5 - 1

Total ways: 2^6 (( 2^5 ) - 1) = 1984