SOURCE

new Vue({
  el: "#example-5",
  data: {
    selected : []
  }
})

<div id="example-5">
   <select name="" id="" multiple v-model="selected">
     <option>请选择</option>
     <option>red</option>
     <option>blue</option>
     <option>yellow</option>
   </select>
  <p>111{{selected}}</p>
  <div v-bind:style={background:selected} class="lgfgf"></div>
</div>

.lgfgf {width: 100px; height: 200px;}