In how many different ways can the letters of the word KNOWLEDGE be arranged in such a way that the vowels always come together?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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  1. In how many different ways can the letters of the word KNOWLEDGE be arranged in such a way that the vowels always come together?
  2. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
  3. From sale force of 150 persons, one will be selected to attend a special sales meeting. If 52 of them are unmarried, 72 are college graduates, and ¾ of the 52 that are unmarried are college graduates, find the probability that the sales person selected at random will be neither single nor a college graduate.
  4. A jar contains 3 red. 5 green, 2 blue and 6 yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a green and then yellow marble?
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