A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 2 choices and the last 3 have 4 choices.
Options
A) 255  B) 448  C) 192  D) 100  E) 144
Two cases.   First Case: 2 Questions - 2 Choices, 2 Questions - 4 Choices   2C2 * 3C2 ways to select the questions   2C1 * 2C1 * 4C1 * 4C1 ways to answer the questions   = 1 * 3 * 2 * 2 * 4 * 4= 
<gadget id="calculator">1 * 3 * 2 * 2 * 4 * 4</gadget>
<output>192</output>
192   Second Case: 1 Question - 2 Choices, 3 Questions - 4 Choices   2C1 * 3C3 ways to select the questions   2C1 * 4C1 * 4C1 * 4C1 ways to answer the questions= 2 * 1 * 2 * 4 * 4 * 4= 
<gadget id="calculator">2 * 1 * 2 * 4 * 4 * 4</gadget>
<output>256</output>
256   Total= 192 +256= 
<gadget id="calculator">192 +256</gadget>
<output>448</output>
448   448
<result>B</result>
A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 2 choices and the last 3 have 4 choices.